Linear Algebra questions and answers in November 2022

. The cross product of two vectors in R is defined by a1 b1 a2b3 - a362 a2 X 62 = a3b1 - a163 a3 b3 La1b2 - a2b1_ Let v = 6 . Find the matrix A of the linear transformation from R to R given by T(x ...

. Do the following for the points (-4, -2), (-3, 2), (-2, 1), (4, -1): (If you are entering decimal approximations, enter at least five decimal places.) (a) Find the equation for the best-fitting pa...

. OT Let x = -3 and y = Use the Gram-Schmidt process to find an orthonormal basis for the subspace of R spanned by 8 a and y. Answer: Hint: Find an orthogonal basis first, then normalize the vectors...

. (6 marks) Let A be a square matrix with characteristic polynomial det (A - XI) = 1+31 -13 (a) (2 marks) Show that A is invertible. (b) (4 marks) Find det(2A + I) and det(2A-1 + I). Hint: For (b), ...

. (6 marks) (a) (4 marks) Let A be a square matrix satisfying A2 = 0. Show that if A is diagonalizable, then A = 0. (b) (2 marks) Find a nonzero 3 x 3 matrix A satisfying A2 = 0. Hint: For (b), try ...

. 3. For each of the following matrices, determine if the matrix is diagonalizable over R and C. If it is, find an invertible matrix P such that P-AP = D , where D is a diagonal matrix. 2 (a) A= 1 2...

. The cross product of two vectors in IR* is defined by bi a2b3 - a3b2 02 = a3b1 - a1b3 a3 b3 a1b2 - a2b1. Let v = 1 . Find the matrix A of the linear transformation from R* to R* given by T(@) =...

Please need an answer to all 4 asap. Do the following for the points (-3, 1), (-1, 2), (0, 2), (3, -1): (If you are entering decimal approximations, enter at least five decimal places.) (a) Find the e...

. Problem 10-05 (Algorithmic) The Metropolitan Bus Company (MBC) purchases diesel fuel from American Petroleum Supply. In addition to the fuel cost, American Petroleum Supply charges MBC $400 per or...

Problem 5. A. Show that the following vectors form a basis of R6 54 LO O 1 0 0 2 57 2 11 b1 = b2 = b3 = b4 = 26 1 5 O -36 0 O 10 O (* ) 216 O 4 0 212 6 b5 = b6 = 96 3 -3 5 B. The following vectors are...

Needs to be answered within 20 min Needs to be answered within 20 min Needs to be answered within 20 min. Let A E Mnxdlﬁ') and let A1, A2, . . . , A}; be the distinct eigenvalues of A. Which of th...

. 19. A small spherical balloon is held in position at the point (1, 2,3), but is free to rotate under the influence of the air current described by the vector field F(x, y, z) = (y - z2, 3x + y + z...

. Suppose W is a subspace of RS. If B - {b1, b2 } is a basis for W, which of the following statements must be true? I. WJ is a three-dimensional subspace of R If. If v e W and ve WJ, then v = 0. III...

all of question 3. 3. Given the vectors in Pz(t) : f(t) = 2t+3. g(t) = 13- 1 with inner product : (f .g) = [of (t)g(t) dt (e) Compute the magnitudes of each vector. (f) Compute the "distance&quot...

Detailed solutions please. L HO (1) (3 points) Set A = 2 4 -1 O (a) Find the eigenvalues for A; and list their algebraic multiplicites. (b) For each eigenvalue for A find a basis for its eigenspace; a...

find the equation relating x,y,z for any vector b = (x,y,z) in the span of the vectors u 1 , u 2 . u 1 = (1, 2, -2), u 2 = (2, 7, -5) the answer is 4x+y+3z = 0 What are the proper steps to ...

how to solve this? Thank you in advance. 822082 qx3zy7 Jump to level 1 Let T : P3 - R be defined by 3ag - 42 + 2as T (an + aix + azz) + agx)) = -ao + 201 - 2as Let u = 2x2 + 23. B - {x3, 23,x,1}. 3do ...

. 8:43:45 160 KB/S To all Xil (31 X Zoom Leave . REC Solve the following operations by showing your steps and information the final answer ON Fat 2122 1. 7/12 - 49/a. Find the value of 's" 2. 1...

. 4. Let hom(V, W ) denote the space of all linear transformations from V to W. Suppose that dim V = n, dim W = m. Prove that hom (V, W) is a vector space (you just need to define notions of additio...

. 4. Let hom(V, W) denote the space of all linear transformations from V to W. Suppose that dim V = n, dim W = m. Prove that hom (V, W) is a vector space (you just need to define notions of addition...

. Consider the parallelepiped P in R determined by the vectors u= 0 1 -2], v= [3 -1 1] and w = [-4 -4 -9]. Use the parallelogram determined by u and v as the base of P. (a) (2 marks) Find the area A...

. (a) (i) Find the transformation matrix for T(w) = proj;(w) where U = NO 2 (ii) Based on the result from part (i), calculate the projection of vector -3 on vector U. L 5 (b) Let us consider a linea...

Answer kindly please and tell which answer for all the questions: . QUESTION 1 1 point Determine whether the following set of vectors is linearly independent or dependent. NO O Linearly dependent...

Solve the following questions: . 1- Find the matrix and, when A = B, the digraph of the relation R. a. A = {1, 2, 3, 4}, B = {1, 4, 6, 8, 9}; aRb if and only if b = a". b. A = {1, 2, 3, 4, 6} =...

. Let W be the set of all vectors of the form shown on the right, where a and b represent arbitrary real numbers. Find a set S of vectors that spans 8a + 3b W, or give an example or an explanation s...

question 1: question 2: Question 3: . (b) Graph only the feasible region. (10%) Click once on each corner point of the feasible region to draw it. Then click on the first point again to close and sh...

Question is in image above.. Suppose u = (4, 2, 4) and v = (4, -4, -3). Then: 1. The projection of u along v is <(-16/sqrt(41)), 16/sqrt(41), 12/sqrt(41)> 2. The projection of u orthogonal to v ...

. Let S = {v1, . .., Un} be a linearly independent set in IF . Which of the following statements are true? Select all true statements. O {v1, ..., Uk} is linearly dependent for k <n. If T : F - F...

. Exercise 4. Let A, B E ﬂ[5(R) such that 446 : B6 : 0. Suppose that 4 and B have the same degree of the minimal polynomials and the same nullity (deg 111A(a?) : deg1113(a?) and dim Ker A : dimKer...

. 7) Given H = [(a,b,c):a - 3b + c = 0,b - 2c = 0,2b - c = 0] a) Find a basis for H. Show and explain why it is a basis. b) State the dimension of H. 6) Find the dimension of the subspace spanned by...

Hi I need help with this I will give the answer full rating . 2 1. Given )2 = —2.r+3 answer the following: a) Write the equation using function notation b) Calculate f (-8) 3 2. Describe, in order...

. Describe all least-squares solutions of the equation Ax = b. 101 1 10 3 1 0 1 17 A= b= 1 10 4 1 10 2 101 6 The least-squares solutions are all vectors of the form x = + Xq with Xz free. (Simplify ...

. 2. Let 7 : R- - R- be the linear transformation satisfying 7 () ) - ()and 7 (:) - (?) Let S : 12 - R' be the linear transformation that scales vectors in the r-direction by 3 and that scales vecto...

(Algorithmic) Quality Air Conditioning manufactures three home air conditioners: an economy model, a standard model, and a deluxe model. The profits per unit are $61, $99, and $135, respectively. The ...

. When applying the Gram-Schmidt process to {{1, 72 ...,ap } to obtain an orthogonal basis {v1, v2, . .., Up } of a subspace W of R", if 1 < k <p, then Vi+1 = Ck+1 - projo, *+1. O True O ...

. Problem 8 $7.2, Exercise 18. Let A be an n x n matrix. List as TRUE all of the following that are equivalent to A being invertible and FALSE otherwise: (a) dim(range(LA)) = n (b) A has n distinct ...

only 6,8,10,16, 19 . 314 Chapter 4 The Eigenvalue Problen 4.5 EXERCISES The following list of matrices and their respective char- product y = Akx for any positive integer k. For in acteristic polyno...

only 3,4,5,6,14,17 Thank you . 4.2 Determinants and the Eigenvalue Problem 1 2 4 12. A = 2 3 7 2 13. A = 4 2 10 23. Let A = (ajj) be the (n x n) matrix specified th 3 dij = d for i = j and al) = [...

. Problem 6. (10 points) Let { u1, u2, us} be an orthonormal basis for an inner product space V and let u = u1 + 2u2 + 2u3, and v = uj +7u3. Determine the value of each of the following: (a) (u, v) ...

Sagara Shoe Group (SSG) is a well-known shoemaker in Indonesia. SSG makes three varieties of boots: Chelsea, Wingtip, and Desert. These boots are made from different combinations of leather and rubber...

2.7 The Singular Value Decomposition and the Pseudoinverse. 8. In the proof of the singular value theorem we claimed that rank T*T = rank T. Verify this by checking explicitly that /(T*T) = N(T). (Thi...

Answer and explain the following question. . Consider the nonlinear system = (x - 1)(y - 2) y = ry + 4 (a) For each equilibrium point, give (i) the equilibrium point, (ii) the linear system at that ...

. 2. (10 points) Consider the unit upper bidiagonal matrix 1 f1 1 f2 U = 1 fn-1 1 (a) Write down an efficient algorithm to solve the linear system Ux = b. (b) Compute the exact number of floating...

How do you solve a question like this?. Determine B, the coordinates of a with respect to B given: 24 53 [ac] B = Hint: x is a linear combination of the vectors in B and the elements of B are the corr...

. Exercise 10.4 An airline operates a fleet of 15 jet aircraft, all equipped with the JET32 engine. The airline performs its own engine-related repairs and main- tenance at its repair facility, The ...

Using a math language like LaTeX, solve the question below. You MUST use a math language for this problem. Thank you! . Solo Practice 17 - Find the least-squares solution of Ax = b. 3 A = 1 -1...

. Problem 6.1. Let A be an m x n matrix, and suppose the CR factorization of A is A = CR, where C is an m x d matrix composed of linearly independent columns of A, and R is a d x n matrix in RREF wi...

. 7) (5.3) The matrix 5 2 --1 -1/2 2 0 0 1/2 1/2 A = 1-1 3 - 1 N 3/2 O 0 4 -1 0 2 -1llo 0 A 1 -1 -1/2 1 1/2 1/2 is factored into the form PDP-1. Use the Diagonalization Theorem to the find eigenvalu...

. ind the equation of the line with the given properties. Passes through (1, - 2) with a slope of - -10 10 (1 -2) -10 . . . he equation of the line is Simplify your answer. Use integers or simplifie...

The program is WileyPlus. I don't know how it wants me to input an answer, I only have one attempt left.. * Your answer is incorrect. Let u = (2,-1) and a = (3,-4). Find the norm of the orthogonal Edi...

. (1 point) A furniture company makes bar stools, tables, and chairs. Each bar stool requires 1 hour of labor, 8 feet of wood, and 0.2 gallons of stain. Each chair requires 4 hours of labor, 16 feet...

An MSU Entrepreneurship team competition winner designed two models of drones to be used by professional photographers. The entry-level drone is called TriCopter, and the higher-end is the PhotoBi...

. Let u . D = -5 Mark all true statements. Ju could be orthogonal to v. O The angle between u and @ is acute (<90 degrees). The angle between u and @ is obtuse(>90 degrees). The vectors u and ...

13. 14. 15. 16. 17. 18. 19. 20. 21. 22. 23. 24. . Find the eigenvalues of the matrix. Tooo 0 7 2 0 0 3 The eigenvalue(s) of the matrix is/are (Use a comma to separate answers as needed.). Find the e...

. Problem 1. Let A 6 FM" be such that the associated linear map T 6 EUR", Fm) has rank 'r. (we are using standard bases.) Prove the following: (a) A has 3'" linearly independent columns. (b...

. 1. (SLO 31 and 32) Find (a) the characteristic equation, (b) the eigenvalues and (c) bases for associated eigenspaces -2 . You should work out (and show) all the details on your own (by hand). for...

Answer and explain the following problem. . Consider the system d I = AT where A = dt 2 (a) Compute the general solution to the system. (b) Compute the matrix exponential edt. (c) Draw the phase pla...

Pls help me sketch it on graph for last question. 11. Given the quadratic relation, V = (x -3)(x + 2) . State the x-intercepts. D. State the x-coordinate of the vertex. C. Calculate the y-coordinate o...

Is the number of tickets sold in column C an absolute quantity or a relative quantity? . Home Insert Draw Page Layout Formulas Data Review View Acrobat Calibri (Body) 11 VA General Paste B ...

. 1. Calculate the determinants of the following matrices. Show the steps of the algorithm clearly or give a clear reason for the determinant using some other properties. (12). a b. 3125 67989 C. 10...

. linear transformation is defined based on the following conditions: . T(cv) = CT(v) . T(utv) = T(u) + T(v) etermine if the following transformation is linear without using specific values. T(x) = ...

. Let A E RX3. Justify your answer to each question. (a) What is the rank of A if nullity A = 3? (b) What is the rank of AT if nullity A = 0? (c) What is the nullity of AT if rank A = 2? (d) What is...

. 3 1) Show that b, = 4 b2 = - 6 a) Show that the set B = (b1, b2, by} is a basis for R3. b) Find the change-of-coordinates matrix from B to the standard basis. b) If [x ]= = =] find the vector x in...

Please answer thoroughly. Do note that this is a three-part question, where its parts are completely independent from each other.. (ﬁ) Find a basis for the subspace VL if 1'1 V={ .172 _ T1+I2+I...

Burdell Distilleries in Knoxville is opening a new facility for its whiskey production. There are 3 machines, a, b, and c. Machine a uses 6 pounds of corn, 18 pounds of barley and 6 pounds of rye to p...

3) The points A(-5,2) , B(-1,6) and C(7,-8) are the vertices of a triangle. a) Determine the coordinates of the midpoint of AB. Label this point P. b) Determine the coordinates of the midpoint of BC. ...

. 2. Define f : P2 + Max2 by f(ax' + br + c) = b a-c a+b (a) (3 points) Find the nullspace for this linear transformation. (b) (3 points) Find the range space for this linear transformation.. (c) (2...

. 1. In this problem A is the 3 x 3 matrix 41 -4 A = 03-2 11-1 i. Show that the eigenvalues of A are the numbers 1, 2 and 3. ii. Find eigenvectors v(1), v(2) and v(3) corresponding to these three ei...

5. (1 mark) Recall that a square matrix is called idempotent if A? - A. Prove that In is the only nonsingular idempotent n x n matrix. 6. (2 marks) Suppose B is the inverse of A?. Prove that. AB is th...

Please Explain. Problem 5. 5. (6 points) Let v1, V2, V3 be the vectors in R' defined by 32 19 25 34 V2. = -3 V3 = -25 36 13 3 (a) Is {v1, V2, V3} linearly independent? Write all zeros if it is, or if ...

. [b - 2d] c) W = 5 + d b + 3d :b, d real 5. Find the matrix A such that the given set is Col A. 2s + 3t r +s - 2t 4r + s :T,s treal 3r - s - -6 6. Given A = w ! 12 a) The nul A is a subspace of Ri,...

Given Problem - . Let Ao, B E Roxn and let A = An + EB for e E R. Assume that A is nonsingular for 0<6<1. (a) Assume that Ao is also nonsingular. Prove that there is a constant C' so that fo...

Please solve the below question. Please explain in details if possible. Thank you for your help. 2. (10 pts) Show that for an LTI system T T( CKCK (t) ) = CK T(XK(t) ). k=1 k=1 You may assume all prop...

using SIMPLEX METHOD, solve the following linear programming problems. subject: math — linear algebra. Rabbits in the laboratories used for drug testing have to be fed a daily diet for accurate re...

please explain. Click on the graph to see an enlarged image. The vector A (blue) has length 9, and makes an angle of g with the x-axis. The vector B (red) has length 5.5, and makes an angle of % with ...

Please explain. Section 4.2 Matrix of Transformations: Problem 14 (1 point) 4 -J 8 Let A 0 and B = OT 9 Find the matrix C of the linear transformation T(x) = B(A(x)). 8 5 C = 9 36 Note: You can earn p...

I need solutions for all of them. Math 2318 Fall 2022 Graded Assignment IV-Due Wednesday November 9th, 2022 Note: There are questions on both sides! ! !! 1) For each of the following subsets of a give...

Hi I need help with #45-63, all true and false, if its false can you please give short explanation. . % In Erereises 45—64. deremrine whether the state- 45. 46. 47. 48. 49. 50. 51. 52. 53. meal...

Hi I nedd help with numbers #1, 3, 9, 11, 13, 15, 21, 23, 29, and 37 please. It's all linear algebra. . 3.1 Cofactor Expansion 209 EXERCISES In Exercises 1-8, compute the determinant of each ma...

Solve all of the arithmetical problems and express each step with written explanations. 3. . 2. Find the linear operator 7 = 7,7 on Ra, where...

. Consider the following vectors in R. X (21, 32, 25) Let A It is known that 1 0 AAT 0 Select all correct statements. For the &chillers select all that apply (x, y. =) is a set of orthogonal vec...

. 0 X WeBWork : Tracogna_MAT_343_( x + C A & https://webwork2.asu.edu/webwork2/Tracogna_MAT_343_ONLINE_B_Fall_2022/Section_4.1_Linear_Transformations/9/?effectiveUser=msymons1.. A Logged in as m...

. WeBWork : Tracogna_MAT_343_( x + X C A & https://webwork2.asu.edu/webwork2/Tracogna_MAT_343_ONLINE_B_Fall_2022/Section_4.1_Linear_Transformations/6/?effectiveUser=msymons1.. A Logged in as msy...

. + X WeBWork : Tracogna_MAT_343_( x C A & https://webwork2.asu.edu/webwork2/Tracogna_MAT_343_ONLINE_B_Fall_2022/Section_3.6_Row_and_Column_space/2/?effectiveUser=msymons. A" Logged in a...

. Suppose I give you four nonzero vectors r, n, c, l'in R2. (a) What are the conditions for those to be bases for the four fundamental subspaces C(AT), N(A), C(A), N(A" ) of a 2 by 2 matrix? (b...

Find the 4x4 matrix for the following sequence of transformations: Start of with Identity matrix, then: first, rotate by π/4 about the z-axis; next, scale by a factor of 3 in the y direction; next, m...

Help me answer the questions please...I have already solved it just trying to make sure my answers are right.. 1 1\ 5) Let A = 1 2 3 3 4 5 a) Find a basis of Col A. b) Find rank A and nul A c) Find a ...

I need this solved please. . CHALLENGE ACTIVITY 2.11.1: LU decomposition. 440884.3014564.qx3zqy7 V Jump to level 1 v 2 Given the matrices below and that A = LU, solve Ax = b. 3 1 -4 -2 -23 A = -5 ...

question 6) please answer kindly.. QUESTION 1 Find the norm of the vector 10v where V = NNN (Round to 2 decimal places if needed. ). QUESTION 5 Find the angle in degrees between the vectors v = and...

I need help with this problem please. . Feedback: CHALLENGE ACTIVITY 2.11.1: LU decomposition. 440884 3014564.qx3zqy7 Jump to level 1 Given that A is transformed into U by the elementary row opera...

I need help solving this please. . CHALLENGE ACTIVITY 2.11.1: LU decomposition. 440884 3014564.qx3zqy7 Start Given that A is transformed into U by the elementary row operations below, complete E, ...

. 5. [HAND IN 12 marks] In the diagram below, the 2x2 shaded square centred at the origin is bounded by the lines x = +1 and y = +1. Let T denote the linear transformation that maps the square on th...

. 5. [5 marks] The (x, y) data points at the right have been observed. It is desired to fit a regression model of the form X y y = ax + B. 0 1 Find the least squares value of a and B and provide the...

. 4.(5 marks) Consider the system of equations: AB = W Here B is the vector on unknowns. To have some common notation, let the columns of A be u and v. Suppose we are given that the least-squares ap...

. Determine if the following sets are subspaces of the real vector space P2 of polynomials of degree at most 2. If the set is a subspace, you must use the subspace theorem to prove it. If the set is...

. (a) Consider the matrix atb b- a M = a - b bta where a and b are real constants. Determine the values of a and b so that (i) M is a symmetric matrix. (ii) M is an orthogonal matrix. (b) Suppose A ...

. Question 2. Consider the system 2x +y + 3z = 5 x - 2y - 8z = 1 3x + 2y + 4z = 3 (a) Try to solve the system using Gaussian elimination. In each step, indicate clearly which elementary row operatio...

. D WeBWork : Tracogna_MAT_343_( x + X C https://webwork2.asu.edu/webwork2/Tracogna_MAT_343_ONLINE_B_Fall_2022/Section_3.4_Basis_and_Dimension/11/ . . . Homework Sets Previous Problem Problem List N...

. WeBWork : Tracogna_MAT_343_( x + X C https://webwork2.asu.edu/webwork2/Tracogna_MAT_343_ONLINE_B_Fall_2022/Section_3.4_Basis_and_Dimension/1/ . . . MAIN MENU Previous Problem Problem List Next Pro...

Hi there, for the three questions above please don't only just answer the questions. I want a detailed explanation as to why the examples you provide fit one of those criterias. Thanks in a...

. 1.Let 2 —'l '1 —6 8 1 —2 —4 —7 8 10 4 —5 —7 0 4 m o.) | .— | O M 0 Find rank(A) 0 Find basis for row(A) c Find basis for 001(A) c Find basis for null(A) 0 Find basis for null(A')...

. Let V = C2 and let C : V - V be the function defined by C(Z1, Z2) = (21, Z2). where if z = a + bi then z = a - bi. (a) Consider V as a vector space with scalars K = C. In this case, show that C is...

The polynomial of degree 3, P(a), has a root of multiplicity 2 at x = 3 and a root of multiplicity 1 at x = - 1. The y-intercept is y = - 3.6. Find a formula for P(ac). P(a) = Question Help: Video Mes...

. 5. (5 points) Describe all eigenspaces of A and state the geometric and algebraic multiplicity of each eigenvalue. Determine whether the matrix is diagonalizable. Justify your answer. If A is diag...

. 4. (5 points) Describe all eigenspaces of A and state the geometric and algebraic multiplicity of each eigenvalue. Determine whether the matrix is diagonalizable. Justify your answer. If A is diag...

. The air in a 67 cubic metre kitchen is initially clean, but when Elaine burns her toast while making breakfast, smoke is mixed with the room's air at a rate of 0.07 mg per second. An air condition...

. 1) Let V be all vectors in the first quadrant in the x-y coordinate plane. V =ly : x20,y 2 0] a) If u and v are in V, is utv in V? b) Find a scalar c such that cv is not in V. c) Is V a vector ...

Reference: practice question from the course material . Problem 5 (20pts). Let A E Rmxn, bE RM, c E R", d'E R be given. Suppose that there exists an TER" satisfying Ax < b. Show that ...