Linear Algebra questions and answers in March 2023

please i need the answer in the proper form. i have provided an additional screenshot to show what the answer should roughly look like for the questions . Question 4 [10 points] exponent form, e.g. ...

. Question 1 [10 points] Evaluate the following expressions, and give your answer in the form a+bi. Use the square root symbol " where needed to give an exact value for your answer. a) (4+2i)+(...

. 3 1 _ : 180 3. Let P : 3 Z ] be the transition matrix for a Markov chain. Let x0 : [ 120 ] be the initial state 5 3 vector for the population. (a) W' hat proportion of the state 1 population wil...

. Question 4 [10 points] exponent form, e.g. '211' Compute the following powers and give your answer in the form a+bi. Use the square root symbol " where needed to give an exact value for your ...

. Question 5 [10 points] Find all distinct roots (real or complex) of 22+10z+29. Enter the roots as a comma-separated list of values of the form u+bi. Use the square root symbol '\l' where needed ...

. 1. An n by n matrix A is said to be a circulant matrix if aij = b(j-i) mod n. For example, three by three matrices are of the circulant if they take the form bo b1 62 A = b2 bo b1 b1 b2 bo (a) Sup...

Don't use internet sources, please help me to solve by yourself . Exercise II (2 X 10 = 20 points) 1. Find the projection of I: = (4. 3, 1, 0) onto the nullspace of the matrix 1 1 1 1 '4—[2 ,1 0...

Don't use internet sources, please help me to solve by yourself. Exercise I (3 X 5 = 15 points) Consider the vectors 61 = (—1,2,2). 62 = (2,2, —l), and 53 = (2, —l,2). 1. Compute the projection ...

pls provide clear working & a screenshot for the graph clearly. Question 1 This question is about the application of linear programming {LP}. Part [h] is a continuation of Part {a}, and Part [e] i...

please do both. 11. A matrix M E Mnxn (C) is called skew-symmetric if Mt = -M. Prove that if M is skew-symmetric and n is odd, then M is not invert- ible. What happens if n is even? 12. A matrix Q E M...

. -3 - 15 0 -15 (1 point) Are the vectors and linearly independent? 3 5 Choose If they are linearly dependent, find scalars that are not all zero such that the equation below is true. If they are li...

s. (1 point) Which of the following sets are subspaces of R.? JA. {(x,y,2) [xty+ 2=0} B. {(4, y, z) | y, z arbitrary numbers } c. {(x, y,z) atytz=7) Do. {(x, y, z) - 4x - 6y = 0, -9x -72 = 0} E. {(r, ...

Linear Algebra with Computer Application Lessons: - Vector Space - Basis of Dimension - Eigen Values and Eigen Vector Directions: Answer the following problems by showing the complete sol...

. 1 1 Time lef't D:3?:'|6 We compute: (b) Find the standard matrix [T] of the lineartransformation T: R" —.> R4 I — 3y + 42 y H 61:: Z —9:{ SEE [T] 2 SEE SEE (c) Find the standard matri...

Linear Algebra with Computer Application Lessons: - Vector Space - Basis of Dimension - Eigen Values and Eigen Vector Directions: Answer the following problems by showing the complete solutio...

. 3. Suppose you are writing a program to model the growth of a bacteria that starts with 5 cells and grows in population by 20% each hour, but instead of using dt dP - 2P, P(0)=5 , you accidentally...

. Given the information below, ﬁnd matrix A. Write your answer as a matrix using the following syntax: square brackets, the entries are listed by rows (with one space between each entry), with the...

Please provide detailed working for the above maths. Question 19 [10 points] Let Ly be the line passing through the point P1=(-1, -2, -4) with direction vector =[-1, 2, -3], and let L2 be the line pas...

Miggy, a millennial health buff, is trying out a new diet regimen that would require him to have an intake of at least 60gms of protein and 30gms of fat per serving of a premix smoothie. Two premix co...

. 1. Theorem (the Cauchy Schwarz inequality). Given any inner product (., .) and induced norm || . ||, the following inequality holds for all , y e R": Kz, y)I < lillyll. Use the Cauchy-Schw...

. Compute the determinant by cofactor expansion. At each step, choose a row or column that involves the least amount of computation. 400 673 200 731 -8 2 (Simplify your answer.) 400 673 200 731 5 -8...

. In mathematics, it is often helpful to understand simple examples first. In this question you will study the behaviour of eigenvalues of 2 >< 2 matrices. Consider a general M : [a b] c: d 1....

not sure how to answer this question. Let A be the matrix . It is the standard matrix of the counterclockwise rotation of R2 around (0, 0) by an angle of . An eigenvector of A is (a) Find the eigen...

I need your help the instructions are bellow and i gived you one of my friends examples what I would like you to do is read his examples and then do similar thing as my friend did but dont copy the sa...

Can you answer in a way where it is easy to copy down on paper . 4. Consider the following matrix game 1 0 A = 0 0 0 a) Verify that A can not be reduced by using domination rules. b) Find the von Ne...

. Compute the determinant of the following matrix A using 3 different meth- ods listed below A = 2 -1 0 2 (a) Compute det(A) by (directly applying) the cofactor expansion along the third row. (b) Co...

What is the value of the objective function at the optimal solution to the LP? Max 8 X + 10 Y + 2 Z Subject To) ...

Make your step by step solution to formulate the given as a LP problem: Miggy, a millennial health buff, is trying out a new diet regimen that would require him to have an intake of at least 60gms ...

If a system of linear equations is represented by the matrix below, what is the solution of the system? Write your answer in this order x, y z. Use a comma (, ) between the answers for x y, and z. (i....

Find a and b so that the following matrix is symmetric. Write your answer in this order: first the value for a, then the value for b. Separate the values by a coma (i e. 4,-10). Do not use brackets Do...

Please show all work, step by step. Thank you so much! . 1. [10] Show (that is, verify all the axioms) that the set of second-degree polynomials defined as, P2 = {p(x)|p(x) = ax2 + bx + c where a, b...

. Q 2 Consider the matrix (a) (1 point) Find a basis for Nul(A). Show your work step-by-step. (b) (1 point) How many vectors are in Nul(A)? Provide an explanation to support your answer. (c) (1 poin...

. 3. [10 pts.] Compute the determinant 2 by reducing the matrix to a triangular one via row or column transformations. (In particular, no cofactor formula.) Keep the following in mind: . Replacing R...

. 1. (a) [3 pts.] If Q, and Q2 are orthogonal matrices, show that Q1Q2 is an orthogonal matrix. [Hint: Use Q Q = /] (b) [4 pts.] Show that if for orthonormal vectors, q1, 92, 93, if "1q1 + 2q2 ...

Prob 1. Let V be the complex vector space of bivariate polynomials of total degree at most 2, and let T be the linear operator T : p 7 → ∂p ∂x − ∂p ∂y . Determine, with proof, (a) the mini...

. 3. (1+3+2+4=10 points) Let N be the subspace of R4 consisting of vectors (:6, y, z, w) satisfying 2m—3y—z+w=0. (a) Consider the sets A = {(1,0,0,—2), (0,1,0,3), (0,0,1,1)} and B = {(—1,—...

Q1) Show work on paper please and thank you. e WHW5V3.pdf X G orthogonal complement - x G linear algebra homework - X Course Hero * *Premier Membership Upg X Course Hero X + X eclass.srv.ualberta.ca/p...

. Prove that this problem is equivalent to its dual. Such LPs are known as self-dual linear programs. Assuming that A is a square matrix, obtain sufficient conditions on C, A, b under which the LP M...

Let v 1 = ⎝ ⎛ 0 3 4 ⎠ ⎞ , v 2 = ⎝ ⎛ 0 − 1 7 ⎠ ⎞ , and v 3 = ⎝ ⎛ − 1 − 4 3 ⎠ ⎞ . Using the Gram Schmidt process,obtain a...

Linear algebra is a branch of mathematics that deals with the study of linear equations, vectors, matrices, and their properties. It is a fundamental tool for various fields such as physics, engineeri...

. Q4. Let A e Man(F). Let {31, . . . , 3k} Q Fm. Let 302- be asolution to A? = 31 for i = 1, . . . , k. (a) Prove that if {31, . . . , 3k} is linearly independent, then {2—51, . . . , 3k} is linea...

. QUESTION 4 Given bases B and B' below.I and vector [x]B- = (1, 1JT, B = {(1.0). (0.11% B' = {(1.1). [5,5]} 1- [10 bis.) What is the transition matrix. F1. from B to I3= 2— [10 bis.) What are t...

. STAR Co. provides paper to smaller companies with volumes that are not large enough to warrant dealing directly with the paper mill. STAR receives 100-feet-wide paper rolls from the mill and cuts ...

Explain your steps. Given 23 10 A = - 50 -22 find an invertible matrix P and a diagonal matrix D so that A = PDP-1. Use the above expression, we can express A? = PD P-1. Enter the 3 matrices below: A7...

DO NOT USE AI TO ANSWER. I WILL REPORT YOU WHEN I FIND OUT. . Exercise 1 (Block Diagonals): Suppose that A is an n X n matrix and B is an m x m matrix. We can use them to form an A O (n+m) x (n+m) m...

. A firm offers three different prices on its products, depending upon the quantity purchased. Since available resources are limited, the firm would like to prepare an optimal production plan to max...

Please help and demonstrate all the required steps. Thanks . Q3 (8 points) Let B be a 5 x 5 matrix with eigenvalues: 11 = 12 = 1 with corresponding eigenvectors s + 2t, $ - t, s, It, -s , s, t ER,...

ving them. Simplify the problem: If the problem seems overwhelming, try simplifying it by removing unnecessary information or breaking it down into smaller parts. DO ENTIRE QUESTIONs ...

Please write on paper neatly and show the steps to solving/understanding this. Thanks!. Problem 3(*): . Let f : R - R be a continuous function. Assume that f(r) = 0 for all rational numbers r. Prove t...

teacher or a tutor, or join a study group to get help from your peers. There are also many online resources and forums where you can ask questions and get help from experts in the field. DO ENT...

group to get help from your peers. There are also many online resources and forums where you can ask questions and get help from experts in the field. DO ENTIRE QUESTIONs ...

to get help from your peers. There are also many online resources and forums where you can ask questions and get help from experts in the field. DO ENTIRE QUESTIONs Read th...

rts. If you are struggling to solve a problem, try breaking it down into smaller parts and tackling each part separately. This can help you identify where you are getting stuck and make it easier to f...

improve your problem-solving skills.Break the problem down into smaller parts. If you are struggling to solve a problem, try breaking it down into smaller parts and tackling each part separately. Th...

considering different approaches can help you find a solution. Learn from your mistakes: If you mistake, don't get discouraged. Instead, use it as an opportunity to learn and improve your problem-solv...

Please answer the following question. Please give a detailed description of your answer. . Consider the vector space V = 02 with scalar multiplication over the real numbers R and let W = {(21,Z2) ...

. Problem 3 (20%) Let A. B E H" be two Hermitian matrices, and both are positive definite. (a) Show that all eigenvalues of BA are real and positive. (b) Let B' = diag(lla; 1. la, 1, ....la, ) ...

. Problem 1 {313%} {a} [10%] It is known that a PSD matrix has a squarevroot factorization. i.e.., A .'1_- {1 iii A = BHB for some matrix E. Find a reierenoe and show that the factorization is uni...

. Exercise 5 Let X1, . . . ,Xn be iid and U([a, b])—distributed with unknown parameters 61 : a and (92 : b. (a) Use the method of moments to derive estimators Tm and T9) for 61 and 62, respectivel...

. Problem 3: Consider the 0,1 knapsack problem defined by max 4x1 + 3x2 + 2x3 + 3x4 subject to 2x1 + 2+ 23 + 24 <3, x 6 {0, 1}4. 1. Use the notion of cover to define an equivalent formulation, an...

. Which of the following sets are subspaces of R3? OA. {(x, y, z) | 5x - 9y - 62 = 7} O B. {(-7ac, -5ac, 9ac) | ac arbitrary number} O c. {(-2, y, z) | y, z arbitrary numbers} OD. {(x, y, z) |x <...

. Definition: In linear programming problems, a constraint is said to be "binding" if its slack variable becomes zero at the optimal solution; otherwise it's called nonbinding. Now, let's ...

. 3. (12 marks) Consider the parallelepiped P in R3 spanned by vectors u = (1, 1, 2), v = (1, 2, 1) and w = (2, 1, 1). Use the parallelogram spanned by u and v as the base of P. a) Find the area of ...

. Let H be the set of all points in the second quadrant in the plane V = R2. That is, H = {(x, y) | x < 0, y > 0}. Is H y a subspace of the vector space V? 1. Is H nonempty? choose 2. Is H clo...

. Let V = R2 and let H be the subset of V of all points on the line 3x - 4y = 0. Is H a subspace of the vector space y V? 1. Does H contain the zero vector of V? choose V X 2. Is H closed under addi...

. Q4. Let A E Mmxn(F). Let { b1, ..., bk} CFm. Let xi be a solution to AX = bi for i = 1, ..., k. (a) Prove that if { b1, ..., bk} is linearly independent, then {{1, ..., Ek} is linearly inde- pende...

. Q3. Let U and W be subspaces of Fr and let T: Fr - F be a linear transformation. Prove/disprove: (a) For all w E W, the set Su = {u EU: T(u) = w} is a subspace of Fr. (b) The set Sw = {u EU: T(u) ...

. Q1. Let A E Mnxn(F). (a) Prove that if A is an eigenvalue of A, then 1 - A is an eigenvalue of I - A. (b) Prove, conversely, that if u is an eigenvalue of I - A, then there exists an eigenvalue &g...

I need solutions for both questions.. 6. Disprove the following statement: If A is an invertible matrix, then A and A- have the same eigenvalues. 7. Let A = 2. Call a line through the origin of R' inv...

. Question 19 (6+4+4) Line , is defined by " -(; )( ). t E R and line Ly is defined by (i) Find the point of intersection of L, and L2, if any. (ii) Compute the distance from P(2, 1,3) to L1. 8...

Can someone please help me solve this problem?. Problem 3. (6 points) Given the matrix C 3 A = 0 find all values of c for which the matrix A is singular. Enter the values of c as a comma-separated lis...

let u = ⎣ ⎢ ⎡ 3 4 5 ⎦ ⎥ ⎤ and v = ⎣ ⎢ ⎡ 1 − 2 2 ⎦ ⎥ ⎤ (a) decompose u into two perpendicular vectors u = u ∥ + u ⊥ , such that u ?...

. $PAR Determine if the subset of R3 consisting of vectors of the form b , where a 2 0, b 2 0, and c 2 0 is a subspace. Select true or false for each statement. V The set contains the zero vector. V...

Please show all work, step by step. Thank you so much! . 6. [12] Given the vector v1 = 21 - 5) in the 2D Cartesian plane, where i and j are the unit vectors along the x and y axes respectively, (a) ...

. we Assignment 8 INWP Assessment Player UI App C education.wiley.com/was/ui/v2/assessment-player/index.html?launchld=8a1c86d3-beec-46be-94... 0 Assignment 8 Question 10 of 13 /10 View Policies Curr...

Please write on paper neatly and show the steps to solving/understanding this. Thanks!. Let f : [0, 27] - R be a continuous function such that f(0) = f(27). Prove that there is an x E [0, 7] such that...

Please write on paper neatly and show the steps to solving/understanding this. Thanks!. Problem 6(*): Let f : [a, b] - R be a strictly increasing function. Suppose that im(f) = [c, d] for some c, d (i...

Find the characteristic equation, the eigenvalues, and bases for the eigenspaces of the following matrix: = 0 Bases for the eigenspaces NOTE: Enter the eigenvalues in increasing order. lambda = boxed ...

. Assume that V is a vector space of dimension n, and {a1, . .., an} and {B, . .., Bn) are two basis. Now we assume that Bj = tjiaj. Then, T = (tij)nxn is called the transition matrix from basis {a1...

. Pick the correct statements on PCA. The variance captured by the first principal component is of / (NV - 1) where N is the number of data points. O PCA based on correlation matrix is unaffected by...

. The row space of a 4x5 matrix is a subspace of R4. Select one: 0 True 0 False. Let ,1 be a 6x6 non—singular matrix. Then the rows of A span the vector space R". Select one: 0...

ath problem, it is important to show your work. Write down each step of the solution and show how you arrived at your answer. This not only helps you keep track of your progress, but also makes it eas...

important to show your work. Write down each step of the solution and show how you arrived at your answer. This not only helps you keep track of your progress, but also makes it easier to check your...

oblem, plan out your solution. This can include sketching a diagram, writing down any equations or formulas you will need to use, and breaking the problem down into smaller, more manageable parts. Pla...

. . Question 1 0/10 pts 07 2 98 0 Details Let T(a + be + cr') = be a linear transformation from P2 to IRS. Is T onto? ? Is T 1-to-1? ? v If not, find a non-trivial element of the null space: Add Wor...

. . Question 1 0/10 pts 0 7 2 98 0 Details Which of the following sets are subspaces of IR ? O 3s IT , SER |r, s,tER, -r + 3s + 2t= 0 Add Work Submit Question Question 2 o/10 pts 9 7 98 0 Details Se...

mathematical objects such as numbers and points exist naturally or are human creations. The mathematician Benjamin Peirce called mathematics "the science that draws necessary conclusions". Albert Ei...

necessary conclusions". Albert Einstein, on the other hand, stated that "as far as the laws of mathematics refer to reality, they are not certain; and as far as they are certain, they do not refer t...

naturally or are human creations. The mathematician Benjamin Peirce called mathematics "the science that draws necessary conclusions". Albert Einstein, on the other hand, stated that "as far as the ...

. 6DA45A96-DE7A-46F0-AB07-CA26EDA5A8FA midterm-2-038b4 #217 Page 3 of 8 Part B: 2 Short answer problems: Provide a full solution to each problem, so write down definitions and explain your steps. Wr...

. 3. Consider the following matrix 3 0 —5 A: g —1 0 1 1 —2 (a) Calculate all of the eigenvalues of A. (b) For each eigenvalue of A found in (a), ﬁnd a basis for the corresponding cigenspace....

-2 4 Compute each matrix sum or product if it is defined. If an expression is undefined, explain why. Let A = 4 5 - 6 3 4 - 3A, B - 3A, AC, CD Compute the matrix product - 3A. Select the correct choic...

separately. This can help you identify where you are getting stuck and make it easier to find a solution. DO ENTIRE QUESTIONs Read the problem carefully: Before you start solvi...

down into smaller parts. If you are struggling to solve a problem, try breaking it down into smaller parts and tackling each part separately. This can help you identify where you are getting stuck a...

part separately. This can help you identify where you are getting stuck and make it easier to find a solution. DO ENTIRE QUESTIO Ns Read the problem carefully: Before you star...

yourproblem-solving skills.Break the problem down into smaller parts. If you are struggling to solve a problem, try breaking it down into smaller parts and tackling each part separately. This can he...

it down into smaller parts and tackling each part separately. This can help you identify where you are getting stuck and make it easier to find a solution. DO ENTIRE QUESTIONs ...

parts and tackling each part separately. This can help you identify where you are getting stuck and make it easier to find a solution. DO ENTIRE QUESTIONs Read the problem carefu...

into smaller parts and tackling each part separately. This can help you identify where you are getting stuck and make it easier to find a solution. DO ENTIRE QUESTIONs Read the...

Don't share my documents. 44. Find the tangent line to the curve F 3 x2 - xy + y2 - 7=0 in the point (2, 3) using the formula for a tangent line to an implicitly defined curve. 4 3 N -4 -3 -2 -1 1 2 3...

. Using row reduction, show that the system of equations cty+z=1 4x + 2y + z =1 10x + 4y + z =1 does not have a unique solution. In fact there is an infinite number of solutions, expressed in terms ...

. Singular Values 5 points possible (graded) Compute a singular value decomposition for the following matrices. Select the number of non-zero singular values for each. 2 3 A = 4 5 6 7 8 O 1 O 2 O 3 ...

. 5. Let T: R3 - R2 be defined by 2x T = 3z N Using the definition of linear transformation, prove T is linear.. 6. Recall from the previous problem the linear transformation T: R3 - R defined by X ...

Addition and Suyog polynomials activity . Why is an Idea Like the Pacific? For each exercise below, add the polynomials. Find your answer at the bottom of the page and write the letter of that exe...

. 5 a Let Haz 1 1/2 1/3 1/2 1/3 1/3 /4 /5 Compute be Hax for x = (1, 1, 1) and x=(0, 6, - 3.6). A small change Ab produces a large change Ax . 5 Compute numerically the largest and smallest singular...

. A linear transformation T: V -> V is nilpotent if there is n > 1 such that: T'" (v) = 0 for all v E V. 1. Give an example of a non-zero nilpotent linear transformation T: R - R3. 2. Pro...

. Question 2 (5 points) Determinants of Vectors -1 N o co 3 8 -4 -12 Let M = O 0 -2 3 -11 O 6 (a) (2 points) Compute the determinant of M using the Laplace Expansion (b) (3 points) Compute the deter...

f. (2 points) You are looking down at a map. A vector u with u = 5 points north and a vector v with |v) = 7 points northeast. The crossproduct u x v points: A) south B) northwest C) up D) down Please ...

and improve your problem-solving skills.Break the problem down into smaller parts. If you are struggling to solve a problem, try breaking it down into smaller parts and tackling each part separately...

. Instead, use it as an opportunity to learn and improve your problem-solving skills.Break the problem down into smaller parts. If you are struggling to solve a problem, try breaking it down into smal...

. (1 point) A square matrix A is idempotent if A2 = A. Let V be the vector space of all 2 x 2 matrices with real entries. Let A be the set of all 2 x 2 idempotent matrices with real entries. Is A a ...

. < Without computing the norm exactly, argue why 100 =( - 100 4 101. 5 What is the inverse of A = (10-190 ) ? What is the condition number of A ? EE 510 Linear algebra Page 1 What is the conditi...

. Exercise 2 (5 x 2 points). Let T: V —)~ V be a linear map (V f.d.). We say that V is simple (for T) if it contains no nontrivial (i.e., at 0, V) invariant subspaces. (1) Suppose T is diagonaliza...

. This exercise is about coordinate systems ($4.4). Let B = The set B is a basis for R2. There exist a unique 2 x 2 matrix P such that [v]B = P-v for all vectors v = Type the (2, 1)-entry of the mat...

For #6 - #11, simply use RREF along with the pivot column/row test to tell me if the linear transformation defined by T(x) = Ax is one-to-one and/or onto. No work need be shown on these, just circle &...

. 3. Matrix A= 2 -1 0 is invertible iff -2 1 5 (a) a+3 (b) a+0 (c) a#5 4. If A is a 4x 4 matrix and det A =2 , then det (3 4) is equal to (a) 6 (b) 162 (c) 48 1 5. If A = 0 2 B = W N then -3 4 (a) A...

Important: you should draw all the distinct labeled spanning trees of G by hand (not just something hard to understand ) . Let G be the labeled graph in Figure 3.22. V1 G: V2 U3 U4 Figure 3.22: ...

. Problem 1: A company operates trucks that sell food. There are 100 trucks in total. There are e routes that can be used, each starting at s and ending at t. To each route, a certain per-truck reve...

relevant information: Identify the given information in the problem that will help you solve it. Circle or underline the numbers or variables that are important.Visualize the problem: Draw a diagram...

trigonometric, etc. Knowing the problem type will help you choose the appropriate formula or method to solve it. Look for relevant information: Identify the given information in the problem that wil...

. 2. Suppose that a and b are odd integers. Prove that there are exactly two integers :1: with 0 3 3: < 140 that are solutions to the following system of congruences in the variable :3. III (mod ...

will help you choose the appropriate formula or method to solve it.Look for relevant information: Identify the given information in the problem that will help you solve it. Circle or underline the n...

Before you start solving the problem, make sure you understand what it's asking. Read the problem carefully and make a note of any key words or phrases.Identify the problem type: Determine what type...

. Read the problem carefully and make a note of any key words or phrases.Identify the problem type: Determine what type of problem it is - algebraic, geometric, trigonometric, etc. Knowing the problem...

Circle or underline the numbers or variables that are important.Visualize the problem: Draw a diagram or graph to help you visualize the problem. This will help you better understand the problem and m...

. Q2. Suppose that a and b are odd integers. Prove that there are exactly two integers x with 0 < x < 140 that are solutions to the following system of congruences in the variable x. x =a (mod...

. 1. A system of linear equations was reduced to the form below. Continue to use Jordan- Gauss elimination to fully solve the system. Show all steps: [4 marks] 013—8 0014 1 —2 6 16] 2. For the f...

. Question 2 10 pts 1 1 0 Details Consider the vectors 7 V1 09 12 5 10 05 Is the set of these vectors linearly independent? O Yes O No If not, find a dependence relation between the vectors. Enter t...

You're free to use your calculator's RREF. - 2 For #1 - #5, let A = -2 , and define T: IR2 - R3, by T'(x) = Ax. Then Tis a linear transformation 3 -6 (I promise). 1. Find T (). See an example. 221 2. ...

. Match each equation with the letter of the graph that most closely resembles the graph of the equation. Assume that a > 1. 1. y = q'+2 2. y = a' + 2 3. y = -a' + 2 4. y = a* +2 (a) (b) (c) (d) ...

. Section 3.2 . (5 points) Q4 (p.161) : . Solution : In Exercises 1-4, solve the equation for X, given that A = 1 2] 3 4 and B = 1 1 1 4. 2(A - B + X) = 3(X - A). . (5 points) Q24 (p. 162) : . Solut...

. . (5 points) Q38a (p.153) : . Solution : cos 0 38. Let A = - sin 0 sin 0 cos 0 (a) Show that A? = cos 20 - sin 20 sin 20 cos 20 - 11. - 1 : - 11 . - 1 5. Section 3.1 . (5 points) Q36 (p.153) : . S...

answers could be correct and . Question 3. Version 1*/1. Score: 0/25 The values of c for which this matrix: C 1 07 0 2 C 1c 5 is invertible are: (-00,-3 ) U(-3,0 ) U (0,3 ) U (3,0 ) x invali...

. Problem 4. (5 points) If |v|| = 5 and |wl| = 3, what are the smallest and largest possible values of the expression ||v - w||? Give a brief explanation of your answer. Problem 5. (3 + 3 + 4 points...

. Problem 3. (5 points) Assume that A, B and C are arbitrary invertible n x n matrices (i.e., A'1,B_1 and 0—1 exist). Explain Why the following identity holds: (ABC)—1 = 0—13-1144. Can you g...

. -2 Find the LU factorization of A = 12 6 0 11 A = To solve the system -3 2 22 12 9 1 X = 86 6 0 11 46 using the LU factorization, you would first solve Ly and then solve O Ux =. To solve the syste...

. H N Co Let A = -1 2 2 4 -6 12 (a) Find the reduced row echelon form R = rref(A) of the matrix A. (b) What is the rank of the matrix A? (c) Find vectors u E R3 and v E R4 such that A = uvT. (d) Fin...

. 1. Let H = Ly : x = 0ory = 0). Which of the following statements is true? (a) H is a subspace of IR2 because cu is in H for all scalars c and all v in H. (b) H is a subspace of IR2 because H spans...

problem carefully and make a note of any key words or phrases.Identify the problem type: Determine what type of problem it is - algebraic, geometric, trigonometric, etc. Knowing the problem type wil...

out, then a mathematics major may interest you. In addition, applications of mathematics are everywhere and a strong background in mathematics can help you in many different careers. DO ENTIRE ...

1) Provide complete solutions in the space provided. 2) Complete questions 4 and 5 using SCILAB. Copy/paste the output or use screenshot and attach it to this assignment.. l. A system of linear equa...

math has practical applications in everyday life. Basic math skills such as addition, subtraction, multiplication, and division are necessary in managing personal finances, cooking, and shopping. Unde...

cooking, and shopping. Understanding mathematical concepts such as percentages, fractions, and ratios is essential when making decisions such as buying a home, investing in stocks, or comparing prices...

prove that it is not linear transformation because T(a) + T(b) not equal to T(a +b). Determine if the following functions are linear transformations. a) T : R3 —) R3, defined by T{x,y,:} = (l,x+ Ly ...

Now, imagine that you want to re-create the second graph for yourself by writing some R code. You want the different "-vores" to be depicted using the shape of points instead of the color of points. Y...

. . Question 5 8 pt You do not need to show your work for this question. Consider the three sets. Select following true statement about each. Set of all vectors where I > y. Set is only closed un...

. Question 3 10 pts 9 1 0 Suppose that A = 2 1 0 . Find the eigenvectors of A (a) Eigenvector with respect to the smallest eigenvalue: v1 = where @1 is a unit vector; (b) Eigenvector with respect to...

Hello, I've been working on a discrete math exercise and I need some input on if I have my logic correct and if any errors are spotted. solution: To prove that the injective map f: X --> Y has exac...

not sure how to answer this question. 4. (12 marks) For each of the following statements determine if it is true or false. If it is true. prove it. If it is false, give an example showing that the ...

. HW9.3. Markov Chain - Steady State - Word problem - Financial Markets Your financial advisor tells you that the behaviour of the stock market from year to year is given by the following Markov cha...

Answer Question 8. Show all work. 8. (35pts) Let A E Maxn (F). Assume that A is similar to a lower triangular matrix (all entries strictly above the diagonal are zero). Prove that the characteristic p...

actical applications in everyday life. Basic math skills such as addition, subtraction, multiplication, and division are necessary in managing personal finances, cooking, and shopping. Understanding m...

action, multiplication, and division are necessary in managing personal finances, cooking, and shopping. Understanding mathematical concepts such as percentages, fractions, and ratios is essential whe...

science, math is used to develop algorithms that help solve complex problems. Apart from its applications in various fields, math has practical applications in everyday life. Basic math skills such ...

algorithms that help solve complex problems. Apart from its applications in various fields, math has practical applications in everyday life. Basic math skills such as addition, subtraction, multiplic...

us understand the world around us. In physics, math is used to express the laws of motion and the properties of matter. In engineering, math is used to design structures and systems that are safe an...

are necessary in managing personal finances, cooking, and shopping. Understanding mathematical concepts such as percentages, fractions, and ratios is essential when making decisions such as buying a h...

. Suppose that V and W are finite dimensional vector spaces. Let a = {V1, V2, . .., Vn} be a basis of V. Prove: A linear transformation T : V -> W is invertible if and only if T(a) = {T(v1), T(V2...

math. Mickey Rats claims that the particular to solution to the following differential equation y + ay = 8 sin ax, a > 0 Must have the following form yp (x) = A cos ax + B sin ax Is he correct? Exp...

. Consider the bases B = {p1, p,} and B' = {q1, 92} for P1, where P1 = 8 + 7%, P, = 8 + 10x, q, = 2, q, =7+ 2x. Find the transition matrix from B to B'. 33 27 The transition matrix from B to B' is Q...

. Question 8 of 21 -15 (ii) determine whether or not the linear system Ax = b is consistent; (iii) find the number of parameters in the general solution of each system in (ii) that is consistent. Si...

. We have two linear mappings T : R'-R, S : R' _>R3 where T is given by the matrix A and S by the matrix B: N - 1 2 -1 A = B = -5 0 21 3 3 a) Find the matrix products AB and BA. b) Find x = T = a...

not sure how to answer this question. 1 0 O 01 0 0 2. (12 marks) Consider the matrix A = 3 1 0 0) 0 1 (a) Find all values A such that det (A - A/) = 0, where A e R and / is 4 x 4 identity matrix. (...

Please can I get an explicit answer. 2. Application: Random walk on graphs - a special case of Markov Chain (Section 2.9) [12] A graph consists of vertices and edges that join two vertices. Graphs are...

Please answer the question below. Thanks very much. The local orchestra has been invited to play at a festival. There are 111 members of the orchestra and 6 are licensed to drive large multi-passen...

Let A ∈ C n×n be a skew-Hermitian matrix, namely such that AH = −A. Show that all the eigenvalues of A are purely imaginary numbers (possibly 0). . Let A e Coxn be a skew-Hermitian matrix, na...

. Question 3 (6 marks). Let A E Rnxn, A = (aij). Assume that ai; 2 0 for all 1 < i, j < n and Et_jaij = 1 for all 1 < j < n. Prove the following statements: (2) The matrix A has eigenval...

Please answer the following question . Let two bases for a two dimensional space be S : {u1,u2} T : {V1,v2}. Say we have the coordinate of a vector w W.r.t 8, hence we have _ a1 [Wis — [ a2 ] W : ...

. 1. Suppose that V and W are ﬁnite dimensional vector spaces, and T : V —> W' is a linear map. Endow V with bases 8, 8', and IV with bases D, 'D'. Show that [T]? = P—1 [T]? Q, where ...

. SAINT MARY'S UNIVERSITY SOBEY MGSC 1205 - Winter 2023 SCHOOL OF BUSINESS Assignment #5 Total Points: 30 points Total Value: 5% of the course final grade Due Date: 1 pm Friday, March 17, 2023 Gr...

d the problem: One of the most important steps in solving a math problem is to understand what the problem is asking you to do. Read the problem carefully and make sure you understand what is being as...

Practice Test: Practice Midterm #2 (Version C) Please provide details and problems thoroughly worked through. Will use as a study guide for exam, exam will present VERY similar questions. Thank You. ...

. Problem 4. Determine whether the following statements are True or False, and provide a short proof (or a counter-example) of your claim. Matrices A and B are in nxn (a) If A and B are orthogonal, ...

Compute the dimension and find bases for the following sets of vectors. (a) Real anti-symmetric 3 x 3 matrices, i.e., matrices A such that A t = − A (b) The polynomials { p ( x ) ∈ P 4 ( ?...

Which of the following sets are subspaces of a vector space? Identify the vector space you are considering, and justify your answer. (a) { x ∈ R 3 ∣ x = ( x 1 , x 2 , x 3 ) s u c h t...

Linear Algebra with Computer Application Lessons: - Applications of System of Linear Equations - Partial Fraction Decomposition Directions: Solve the partial fraction decomposition of the rational...

. Math 220 Spring 2023 Written Homework 5 Answer Key 1. (a) ' ] 4. (a) -1 2 (b ) 3/10 -1/5 -1/47 [1/4 (c) 2 7/4 + 1/4 1 0. Math 220 Spring 2023 Written Homework 5 Be sure to show all your work inclu...

Problem 1 and 2: . problem #l a ) ( Col A) 1 X 2 olumn space of A b ) The column space of A is a live ( single vector) in TRE subspace of TR 2 ( ) AX = 0 XL ENUI(AS A X1+2X2+3X3=0 = X1=-2X2...

I need help with this question. PLEASE DO NOT SUBMIT OTHERS WORK. I WILL THUMBS DOWN!!! I NEED A NEW ANSWER. THANK YOU . Use Frobenius method of Lecture 11, to find the first three non-zero terms ...

Im having trouble with this question. Please show the work step by step using the modified Euler method. Thanks . Use the modified Euler method of Lecture 4, with n = 10, to find x(1): dx dt = 22 - ...

. If A a b C then A is invertible if ad - bc # 0, in which case A- 1 = 1 -b ad - bc -c If ad - bc = 0, then A is not invertible. Find the inverse of the given matrix (if it exists) using the theorem...

. Further Exercises 7.6 1. Let's look at a different parameterization of the Higgins—Selkov model, 5' = v0 — 0.235132 P' = 0.235132 — 0.4P a) Regardless of the value of V0, this system has...

Given the following inequalities. A) Determine the y-intercept B) Determine the slope C) Graph the inequalities using their slope and y-intercept 1) y >= x + 1 2) y < 2x = 4 3) 2y - 4 > ...

up with a solution. Be organized: Keep your work organized and tidy, making it easier to double-check your calculations and identify any mistakes. Practice good time management: Managing your time wel...

these two questions. thank you. for question 2 use the modified euler method.. Find the general solution: " +x - 2x = et Use the modified Euler method of Lecture 4, with n = 10, to find x(1): dt ...

. Let k, h be unknown constants and consider the linear system: 6y 5z 6 - 5y + 3z = -2 -19x + 28 y + hz = k This system has a unique solution whenever h * If h is the (correct) value entered above, ...

Linear Algebra Final answer only - No Explanation . Section 3.6 Row and Column space: Problem 2 (1 point) A N LAN Find a basis for the row space of A, a basis for the column space of A, a basis...