Linear Algebra questions and answers in August 2023

Question 18 1 pts Suppose T is a solution to Ax = 0 for an 2 by 2 square matrix A. Which statement is false? If Ax = is consistent, then the solution may be unique. O A is not invertible. There is a s...

Perform the row reduction algorithm to TRANSFORM the following augmented matrix into reduced echelon form. Show and label all steps, matrix to matrix. Write the general solution in para- metric form f...

If the following linear system is consistent, FIND the general solution (meaning a list of the values of the variables) indicating any free variables. Otherwise, show that there is no solution. Show a...

Find a value of k for which the matrix is singular. Explain your reasoning with Gauss-Jordan Elimination. . Find a value of k for which the matrix 2 1 - NO 1 2 1 k 0 -3 is singular. Explain your rea...

I need help with this linear system. Thanks in advance! . Find (if possible) conditions on b such that the system has no solution, one solution, or infinitely many solutions. 3x - y + 2z =3 xty -...

Find N(A) and describe it as all linear combinations of some vectors (you must find these vectors). . Let 0 2 1 B = 2 0 0 2 2 -2 Find N(B) and describe it as all linear combinations of some vectors...

help me with this please . Consider this system of equations: 3m' —|— 9.7:_ = 57 2m'+ac_ = —1 A. Write the corresponding augmented coefficient matrix. To enter your answers, click in the...

(a) Find the reduced row-echelon forms of the following two matrices: (b) Find N(A) and describe the space as all the linear combinations of its special solutions. (c) Find N(B) and describe it as a...

. (10 points) Find the particular solution Xp to the following equation, which comes from setting all of the free variables to 0. 2 9 -2 -17 -3 -6 -3 -27 4 Xp = 37 -4 -2 -18 8 62 0 C 3 = 0 4 = 0 0. ...

I need help on 9. a webassign.net 9. [-/5 Points] DETAILS LARLINALG8 2.2.043.SBS. MY NOTES ASK YOUR TEACHER Verify that (AB) T = BTAT. A = N and B = STEP 1: Find (AB) T. (AB) T = STEP 2: Find BAT. BTA...

. (10 points) Find the particular solution xp to the following equation. which comes from setting all of the free variables to O. 1 2 1 9 *2 717 73 76 73 727 4 xp: 37 *2 *4 *2 718 8 62 931: $2: $3: ...

. (10 points) Find the particular solution xp to the following equation, which comes from setting all of the free variables to O. 1 76 71 5 0 0 0 0 0 U 0 0 $1: $2: $3: $4:. Problem 8 and 9: The prob...

Question (1) Find three independent vectors u, v, w, that each lie in N(A) , the null space of (A) Question (2) : Find the value of r for which . 2 2 1 2 (1 point) Let A = -4 -4 -2 -4 Find thre...

Hi, I need Help Kindly give stepwise solutions for both parts with an explanation. and please attach a clear image so that I understand. Thanks!. Question 2) Given the matrix A with an unknown a ...

. Using the graph shown below, figure out everything you can about the motion. 0 Velocity (mls) Justify your steps below. Hint: Remember that slope = AWAX (rise "over"run), and: - slope of a ...

Can you please answer this question? I am also attaching Theorem 3.4.3 . 4. a. Find the general solution to the linear system and confirm that the row vectors of the coefficient matrix are orthog...

. 2. Consider the matrix N 2 3 4 A = 1 4 (a) If this is the augmented matrix of a system of linear equations, how many equations and how many variables are there? (b) Use row operations to write a (...

. 3. Linear combinations: (a) What does it mean to say that the vector b is a linear combina- tion of the vectors a, and a2? (b) Show how to write as a linear combination of W N - and 0 or explain w...

. 2. (10 points) Consider the linear system (where o and B are constants): x+ 3y+z=a Ax+ y+ z =-1 2x + 3y +4z =3 Find conditions on a and/or B such that: (a) The system has a unique solution. (b) Th...

L11 Exercises: Möbius Lesson 11B Homework . Graph the following system of equations. I- y= 2 21+y =1 What type of system is this? O Inconsistent () Independent () Dependent Solution I= Number Numbe...

Need helping answering this and please explain why, thank you. Row reduce the matrix to reduced echelon form. Identify the pivot positions in the final matrix and in the original matrix, and list t...

. 4. Determine whether (he set of all 2 x 2 invertible matrices with the usual operations of matrix addition and scalar multiplication is a vector space. If it is not a vector space, identify the ve...

Need help understanding the process of solving these matricies. . ConSider the accompanying matrix as the augmented matrix eta linear system State in words the next two elementary row operationsthat ...

Can you please help me to determine the correct option If A is a 2x3 matrix, it is correct that options : 1 - is a matrix of order 2x3 2- is a matrix of order 3x3 3- is a...

. If S = {v1, ..., Vn} C R" is a collection of vectors, A = [v1 . . . (Vn], and A is an invertible matrix, then which of the following must be true (select all that apply): The transformation T...

. The following data has a linear relationship. Copy and paste the data into Excel. Use Excel to find the equation of the linear trendline. X y 9 216 5 149 6 189 17 395 10 208 1 52 6 144 20 383 9 23...

. 8. For the function f(x) = = 17*+2 -2, a) What is the base function? (1 mark) b) Use point mapping rule to draw the graph of f(x). Make sure to label scale and asymptote. (3 marks) c) State the do...

If it is a linear combination, determine a non-trivial linear relation. (A non-trivial relation is three numbers that are not all three zero.) Otherwise, enter 0's for the coefficients. . Let A = 0 ...

. (6 points) Let A = 6 8 3 Find a nonzero vector v in /( A), the null space of A, and a nonzero vector w in C(A), the column space of A. U = W =. Let u = (-3, 6, 1), v = (4, 7, 5), w = (6, 33, s + 6...

. (7 points) Suppose that: 1 2 -1 2 A = and B = 5 -1 2 2 - -5 2 4 Given the following descriptions, determine the following elementary matrices and their inverses. a) The elementary matrix E21 subtr...

What is the reduced row echelon form reduced row echelon form=rref(A)of the following matrix?. (1 point) What is the reduced row echelon form R = rreﬂA) of the following matrix? —2 2 22 A = —ﬁ...

. l l. A small manufacturing plant makes three types of inﬂatable boats: one-person, two-person, and four-person models. Each boat requires the service of three departments, as listed on the table...

Can anyone please help me with this question please? I'm stuck on it!. 6. [-/1 Points] DETAILS POOLELINALG4 1.2.020.EP. Let 0 be the angle between u and v. u = [8, 7, -1], v = [1, -1, 1] Find cos(0). ...

Question 1 Find A − 1 If A is invertible by using Gauss-Jordan Elimination, Otherwise, explain why it is not invertible (This matrix is 3 rows X 3 columns) A = [ 2 -1 -6 ] ...

Can anyone please help me with this question please?. A parallelogram has diagonals determined by the vectors below. Show that the parallelogram is a rhombus (all sides of equal length). Since d, . d,...

A store used two different price values for their student backpacks to approximate the supply and demand equation. The linear demand equation is: 𝑝 = −0.75𝑞 + 42.5 and the linear supply equ...

How do I study math? This is a really bad question and I know I'm putting myself out here like this, but I'm in the eleventh grade and don't understand 5th grade-6th grade math. My understanding of ma...

Jacob rides his bike at 15km/h along a 30km trail. His distance, D, in kilometres, from the trail's end at time t hours may be modelled by the equation D = 30 - 15t. Felicia rides at the same speed as...

Can you please answer this questions with all the detailed steps?. 5. a. Find the area of the triangle in 3-space that has vertices P(1, -1, 2), Q (0, 3, 4) and R(6, 1, 8). b. Given u = (-1, 2, 4), = ...

Can you please answer this with all the detailed steps?. 3. a. Find the distance between the given parallel planes 2x-y+z=1: 2x-y+2=-1. b. i. Show that 7 = (a, b) and w = (-b, a) are orthogonal vector...

Consider the system of Linear equations x + y = 􀀀1 2x + 2y + 2z = 3 3x + 4y + 5z = 􀀀2 Use LU factorization to solve for the unknowns. Or state if it is not possible. (a) Write the LU factoriza...

Find the LU factorization of A . -2 1 Find the LU factorization of A = -2 5 3 2 -17 -18 and use FORWARD SUBSTITUTION AND BACKWARD SUBSTITUTION to solve the system -2 1 -1 C1 -12 -2 5 3 -12 2 -17 -18...

use FORWARD SUBSTITUTION AND BACKWARD SUBSTITUTION to solve the system. (1 point) -3 -2 Find the LU factorization of A = -9 -10 and use FORWARD SUBSTITUTION AND BACKWARD SUBSTITUTION to solve the sy...

250 200 176 150 718 Yards 100 90 55 50 Vikings 14 Rams Pirates To Cadets -6 A -50 Teams Yards Passing Yards Rushing Q Using the bar graph from above to answer the following questions: a) Which team ga...

The temperature, f(t) of a cup of coffee after t minutes can be determined by the equation f(t) = 76(0.93) A graph of the function f(t) is shown below. 80 f(t) 70 60- 50- 40 30 20 10 10 15 20 Estimate...

Only do problem 3. Use problem 2 for context solve using Cramer's rule show all work thank you OSO. Given: The following set of simultaneous equations using matrix inversion. Include 6X + 7Y+ 18Z = 12...

. Given: The following set of simultaneous equations using matrix inversion. Include 6X+ 7Y+ 182: 12 2X+122+9Y=16 12Y— 72+ 7X: 23 Determine: The solution for X, Y and 2 using matrix inversion. You...

Can you please answer this with all the details? . 5. The following plane is in 3-space with equation that passes through three noncollinear points (21, 31, 21). (12, 1/2, 22) and (C3. ya, 23) is giv...

Please help with math. 3. Solve the absolute value equations algebraically. -Verify each solution using substitution or graphically (show work either way). a) |3x - 1| = 20 b) 1-x2 + 6x -121 =7 c) |x2...

Please help. Name 1. Use the graph of y =f (x) to sketch the graph of y = If (x)| on the same coordinate grid. State the domain and range of If (x)| a) b) NW - 5 - -6 -5 -4 -3 -2 -1 0 2 3 4 5 6 - x -1...

Can you please solve all the questions under A and B. Please make sure to provide detailed solutions. 3. a. Find the values of k for which the matrix A is invertible. 2 0 A =kik 0 1 b. Given a 4 x 4 m...

can you please solve this and provide all the detailed steps. 2. a. Evaluate the determinant of the matrix by first reducing the matrix to row echelon form and then using a combination of row operatio...

. Section 1.1 Systems: Problem 2 (1 point) For each system, determine whether it has a unique solution (in this case, find the solution), infinitely many solutions, or no solutions. J-51 + 5y = 40 -...

Thanks . Fertilizer is sold in 100 pound bags labelled with the amount of nitrogen ( N), phosphoric acid ( P205), and potash ( K20) present. The mixture of these nutrients varies from one type of fe...

. 0 points Suppose B = {u1, u2, u3 } is a basis for a vector space U, where U1 = Use THE GRAM-SCHMIDT PROCESS basis and an orthonormal basis of U. I understand that I must submit my organized writte...

. Imported From IE Top Shelf Q Suggested Sites rom IE 01 Time 1 0 points If u and v are in R", show that span{u, v} = span {2u + 3v, 4u -50}.! I understand that I must submit my organized writt...

JUST B + C, not A is needed. THANK YOU. 5. Use Gauss-Jordan elimination to find the solution set to the following linear systems. 5x, + 3x2 = 1 a. -3x1 - 2x2 = 4 2x1 + 3x2 - X3 = -2 b. 4x1 + 5x2 - 3x3...

Find values of a, b, and c. Type only answers in order a, b, and c without typing a, b, and c. Separate answers by a comma, No Space, No Brackets. For example: 2,3,4 [3 Marks] Find Adj(A). Ty...

. 1) Calculate the volume of the parallelepiped created with the vectors below. [2 marks] 2) Establish whether the following vectors having a common initial point are placed in the same plane. u = (...

. Question 6 (5 points) E-II Given the following vectors: u = (-5, 0) and v = (1, 6), find: a) II 471, ll —3 H '0 "(Express your answers rounded to two decimal places) [2 marks] b) Projection ...

. Name: Date: Unit 7: Geometry Per: Homework 11: Translations ** This is a 2-page document! ** ates . thrections: Graph and label each figure and its image under the given translation. Then, give 1....

To solve the equation: 24 (34 + x) = 1, 200, give the reasons Step 3: 24x = 384 for each of the given steps. What was done to the previous step to Step 4: x = 16 get to the current equation? (1 point)...

How would I add the vectors for a linear algebra question and separate them to show a linear transformation to determine if F: R 3 --> R 2 ? My work is attached. Thank you. F X, 3 x, + *2 - 6X...

. Consider the following. 9010 A = 091 1 0 017 0 0 8 0 (a) Compute the characteristic polynomial of A. O. Summary + det(A - )I) = (2 + 7 ) (2 - 8) (2 - 9)2 (b) Compute the eigenvalues and bases of t...

. Consider the following matrix A = [V V V3]. A = AHAHAH W / N W / H W / H O. Summary + Find the following dot products. V 1 V, = 0 V. 10 . V2 10 V 1 . V 1 3/16 1/2 2/3 Determine whether the given m...

. 2. . Find the eigenvalues and normalized eigenvectors (i.e. length of l) for the following matrix: Show that the dot product of the eigenvectors is zero and therefore orthogonal. In two to three s...

. 4 0 04 A = 0 541 0 0 50 0 0 List the eigenvalues of A and bases of the corresponding eigenspaces. (Enter your answers from smallest to largest eigenvalue. Repeated eigenvalues should be entered re...

. Consider the following. O. Summary + 1 1 0 A = 0 -4 1 0 0 5 (a) Compute the characteristic polynomial of A. det(A - )I) = - (2 - 1) ( 2 + 4) (2 - 5) (b) Compute the eigenvalues and bases of the co...

. Consider the following. 1 1 0 A = 0 -4 1 0 0 5 (a) Compute the characteristic polynomial of A. det(A - )I) = O. Summary + (b) Compute the eigenvalues and bases of the corresponding eigenspaces of ...

. Find all (real) values of k for which A is diagonalizable. (Enter your answers as a comma-separated list.) O. Summary + A = 3 2 OK k # Need Help? Read It. Find all (real) values of k for which A i...

. Consider the following. 4 0 04 0 541 A = 0 050 0 0 01 O. Summary + List the eigenvalues of A and bases of the corresponding eigenspaces. (Enter your answers from smallest to largest eigenvalue. Re...

. A diagonalization of the matrix A is given in the form PAP = D. List the eigenvalues of A and bases for the corresponding eigenspaces. (Repeated eigenvalues should be entered repeatedly with the s...

. Consider the following matrix A = [v1 v2 v3]. Determine whether the given matrix is orthogonal. The matrix is orthogonal. © The matrix is not orthogonal. «I Find its inverse. (If it is not ortho...

. 2 Let P= -3 -5 0 V = Complete parts (a) and (b). 4 6 . . . a. Find a basis fu1, U2, Ug) for RS such that P is the change-of-coordinates matrix from (U1, U2, Ug) to the basis (V1, V2, V3). [Hint: W...

. Final Exam MML Testing Session | ProctorU C . mylab pears s=opted in&wl access_date=2023-07-07109%3a16%3a32.856522+00%3800&context_parent_id-61915954 Summer 2023 Linear Algebra (MATH-2418-...

. tent/PlayerTest aspx.wlaccess_status-opted in&wl_access_date=2023-07-07109%316%3a32.856522+00%3a00&co Summer 2023 Linear Algebra (MATH-2418-43740) khaled Al Sheplak 02/12 23 52 PA Test: Fi...

. 495586.3410486.qx3zqy7 Jump to level 1 4 6 For the matrix A : 1 find the eigenvector corresponding to each eigenvalue given. 3 Eigenvalue: 1 = 2, Eigenvector: Eigenvalue: ) = Ex: 5 + Eigenvector: ...

i used matrix 4 8 8 16 please show if this matrix works for the formula as you get an eigenvalue of 0. if this matrix does not work please provide an answer that does. . 2. Construct a...

use the matrix 4 8 8 16 please also show and explain why the eigenvalue of 0 does not satisfy the formula . 2. Construct a 2x2 matrix A and verify the following formula: tr(A) = 1 - det(A...

. Do the given vectors form an orthogonal basis for R2? w O Yes, the given set does form an orthogonal basis for R2. O. Summary + O No, the given set does not form an orthogonal basis for R2. You ar...

. Find the dot product of each pair of the given vectors. O. Summary + V1 = ANN N 8 2 Determine if the given vectors form an orthogonal set. O These vectors form an orthogonal set. O These vectors d...

. Consider the following. O. Summary + 4 0 5 A = 6 6 5 (a) Compute the characteristic polynomial of A. det(A - )I) = (b) Compute the eigenvalues and bases of the corresponding eigenspaces of A. (Rep...

. Consider the following. A = 1 6 -2 9 (a) Compute the characteristic polynomial of A. det(A - )I) = (b) Compute the eigenvalues and bases of the corresponding eigenspaces of A. (Repeated eigenvalue...

Can I have help with this please?. -16 a B The matrix A = 22 15 6 has an eigenvalue ) = 1 with algebraic multiplicity 2 and geometric multiplicity 1. 19 13 8 (a) Find the last eigenvalue and provid...

Can I have help with this?. Let A be a 11 x 11 matrix which has only one eigenvalue 1 = 2. Let dk = nullity(A - 21)k. Given that the sequence d1, d2, d3, . . . is 5, 7, 9, 11, .. . Suppose that A has ...

Can I have help with this please?. The matrix A has a Jordan form J2 (7) @ J2(7) @ JA(7) @ J5(-5). Pick all the Jordan matrices which are similar to A from the following list. O J5 (7) @ JA (7) DJ2...

Can I have help with this please?. Question 1 Part (1) [6 marks] (a) Choose all correct statements: Let U be a hyperplane in R given by 8x] - 4x2 + 5x3 + 6x4 = 0. The map T : 1R4 _ 1R4 , where T...

. Determine the dimensions of Nul A, Col A, and Row Afor the given matrix. 130 54— A= 010—45 00012 The dimension of Nul A is (Type a whole number.) The dimension of Col A is (Type a whole num...

. Matrix A is factored in the form PDP" . Use the Diagonalization Theorem to find the eigenvalues of A and a basis for each eigenspace. 4 0 - 12 -60 -1 60 0 0 0 1 A = 1 6 6 36 = 0 1 3 0 6...

. Find a basis for the eigenspace corresponding to the eigenvalue. 6 3 —3 A= —2 —1 6 ,9»=5 2 6 —1 A basis for the eigenspace corresponding to A: 5 is {E}. (Type a vector or list of vecto...

. W . 4 3 3 Is V= - 2 an eigenvector of A = 2 -3 -2 |? If so, find the eigenvalue. 0 . . . Select the correct choice below and, if necessary, fill in the answer box within your choice. O A. Yes, v i...

. Let B = {b1,b2} and C = {c1422} be bases for R2. Find the change-of—coordinates matrix from B to C and the change-of—coordinates matrix from C to B. Find the change-of—coordinates matrix ...

. Determine if the set of vectors shown to the right is a basis for R3. If the set of vectors is not a basis, determine whether it is linearly independentand whether the set spans R3. 3 —1 1 4 —...

. Let V be the set of vectors shown below. x V: :x20,y<0 y a. If u and v are in V, is u +v in V? Why? b. Find a specific vector u in V and a specific scalar c such that cu is not in V. —E—...

. Find the 3x 3 matrix that produces the described composite 2D transformation below, using homogeneous coordinates. Translate by ( — 6,4), and then scale the x-coordinate by 0.6 and the y-coordin...

. Suppose an economy has four sectors: Mining, Lumber, Energy, and Transportation. Mining sells 20% of its output to Lumber, 70% to Energy, and retains the rest. Lumber sells 15% of its output to Mi...

What is the basis for the orthogonal complement of the subspace of R spanned by the vectors. V1 = (1, 3, -3, 5), V2 = (4, 11, 1, 3), V3 = (1, 2, 10, -12) The basis for the row space isWhat is the basi...

1. Give the homeogeneous linear system, X1 - X2 + 3x3 - X4 = O 2x1 - 8X2 + 6x3 - 2 4 = O find a basis for the solution space of the homogeneous linear system and find the dimension of the solution spa...

Please help me with the following questions. 1. L=______ L=_______ 4. . Find an LU factorization of the matrix A (with L unit lower triangular). 3 -6 A= 1 12 -22 10 - 11 U = (Simplify yo...

. Let P3(R) be the vector space of all real polynomials of at most degrees 3 with the inner product defined as (f, g) = [ f(x)g(x)dx. (a) Find an orthonormal basis B for P3 (b) Consider the linear o...

. 4. (a) Let T : R2 -> R2 be rotation by 7/3, i.e. T(x) = the rotation of x by 7/3 around 0. From your answer to 3(f), without computing any matrices, what would you expect det(A) to be? (Does T ...

Please help me witht the following questions. 1. 2. 3. 4. 5. . Classify the quadratic form below. Then make a change of variable, x = Py, that transforms the quadratic form into one...

. QUESTION 6 For each of the following pairs of matrices A, B E M2x2(C), explain whether they are similar, unitarily equivalent or neither of the two. (6.1) A = (6.2) A = 1 0 , B- 9 0' (6.3) A = 0 1...

. QUESTION 3 Let V be a finite-dimensional inner product space and let y, z E V be non-zero vectors such that y I z. Define T : V - V by T(x) = x - (x, y)z for all x E V. 21 (3.1) Find the eigenvalu...

. QUESTION 2 Let X1 - X2+X3= 3 3X1 + X2+ X3 = 3 .(i) (2.1) Find the minimal solution u E R3 to the system. (2.2) Express the general solution to (i) in the form x = v + wt where t is a parameter and...

. QUESTION 1 Let 7 : C3 - C3 be the linear operator defined by T(Z1, Z2, Z3) = (Z1 + iZ2, iZ2 - Z3, Z1 + Z3). (1.1) Find a formula for T*(Z1, Z2, Z3) expressed as a single vector in terms of Z1, Z2,...

Please help me with the following questions. 1. 2. 3. 4. . Points: 0 of 1 Diagonalize the following matrix. 7 -40 4 0 41 - 4 0 0 3 0 0 0 0 Select the correct choice below and, if necessa...

Determine whether the set of vectors is orthogonal. Show all of your work, and state "yes" or "no" ⎣ ⎢ ⎡ − 2 0 − 4 0 − 2 0 ⎦ ⎥ ⎤ , ⎣ ⎢ ⎡ 2 0 0 − 2 0 ...

. Suppose the characteristic equation for a matrix A is given by 13 - 412 - 161 + 64 = 0. Find the eigenvalues of the matrix A and give the algebraic multiplicity of each eigenvalue. Eigenvalue: 1 =...

. 7 6 The matrix A = has eigenvalue >1 = 4 with corresponding eigenvector and 3 2 eigenvalue 12 = 1 with corresponding eigenvector Use this information to fill in the following matrices for the d...

. CO 0 7 4 3 Give the algebraic multiplicity of each eigenvalue. Find the eigenvalues of the matrix A = 0 0 6 1 Eigenvalue: 1 = Eigenvalue: 1 = 6 Algebraic multiplicity: Algebraic multiplicity: Ex: ...

Please someone help. Center IN X (0. 20) (-3052, 0) X desmos 4) Label the following points of interest on your graph. You may draw them by hand. i) vertex ii) roots ili) axis of symmetry iv) y-interce...

. 4. Find a condition on the numbers a, b, c such that the following system is consistent. 3.x -y +2z = a ty -2 = 2.x -2y +32 = C (5 marks) 5. Find values of k if any that satisfy the equation [ k 1...

. 6. Find the inverse of the matrix for a non-zero k using Gauss-Jordan elimination 100 0 01 k 0 0 01 k (10 marks) 7. Assuming A is a square matrix that satisfies the condition A2 - 3A + 21 = 0, fin...

May someone please walk me thru this question?. X Center: Cool Wich 20818 Quagity 1 X (0, 2.0) (-2 082, 0) (2:087, 0) Cosmos 5) Use the quadratic formula to show the roots from the standard form of yo...

. Use Cramer's Rule to solve the given linear system. (If there is no solution, enter NO SOLUTION.) 3x - y = 17 x + 4y = -3 ( x, y ) = Need Help? Read It. Use Cramer's Rule to solve the given linear...

. Find the determinant, assuming that a b C de = 6. g 5c b a 5f e d 5i h g Need Help? Read It Watch It. A square matrix A is invertible if and only if det A # 0. Use the theorem above to find all va...

. Compute the determinant using cofactor expansion along the first row and along the first column. 0 1 Need Help? Read It. Compute the determinant using cofactor expansion along any row or column th...

. Find all of the eigenvalues 1 of the matrix A. (Hint: Use the method of Example 4.5 of finding the solutions to the equation 0 = det(A - )1). Enter your answers as a comma- separated list.) A = 3 ...

just answer question 3. Q1 [4 marks] a) Explain what it means that the matrix Q E Mnn (R) is orthogonal. b) Prove that Qax . Qay = x y, for every x, y E R2, where Qa = sin a cosa E M2,2 (R), and a E R...

How do I solve this? . Let A be a 12 x 12 matrix which has only one eigenvalue 1 = 5. Let dk = nullity(A - 5 1)k Given that the sequence dj, do, d3, . . . is 4, 7, 9, 11, 12, ... Suppose that A has ...

How do I solve this? . Question 2 Part (II) [5 marks] The curve 52 x2 + 72 x y + 73 y2 = 2500 in R2 is written in the form of x/Ax = 2500, where 52 36 X = and A = 36 73 The symmetric matrix A can be...

How do I solve this? . For this question, you must enter non-integer numbers as fractions. Do not use decimals. 16 -9 Let X1 = = -5 , X3 -35 , and write W = span {x1, X2, x3} 18 5 (a) To apply the G...

How do I solve this? . Question 1 Part (III) [4 marks] The subspace U of IR is spanned by the vectors -2 u = and u2 = Let U- be the orthogonal complement of U. A Suppose that V = is a vector in 1R4....

How do I solve this? . Question 1 Part (II) [4 marks] (a) Suppose that U is a subspace of IR4 and dim(U) = 3. Geometrically, U -, the orthogonal complement of U is o {o} O a line. O a plane. O a hyp...

. 7. Let (.) be the integral inner product on C [-1, 1]. That is, given f = f(x) and g = g(x), we have (f, g) = [ f(x)g(x)dx. Determine whether or not f = f (x) = sin x and g = g(x) = cos x are orth...

. 4. Find a condition on the numbers a, b, c such that the following system is consistent. 3x -y +2z = a ty - z =b 2x -2y +32 = c (5 marks) 5. Find values of k if any that satisfy the equation 1 1 K...

. 2. Find a cubic polynomial whose graph passes through these points (1, 3), (2, -2), (3, -5), (4, 0). State the system of equations you will be solving, and then use Gauss or Gauss-Jordan eliminati...

. 1. (4 points) Using interval notation, state the domain of the piecewise-defined function below. 2x + 8x2 if x < -30 k (a ) = if - 30 < x < -10 18 if x > -10 2. (3 points) Using interv...

I don't understand why I got partial credit for this one. Please help. Thank you. Question 3 0.8/2 pts O 2 2 19 0 Details Score on last try: 0.8 of 2 pts. See Details for more. Get a similar questi...

How to graph this? When I try graphing it even when it is correct, it is giving me only partial points. . Question 5 1/2 pts 5 # 15 0 Details Move the arrow below to visualize the vector V Moving a po...

i don't understand why b is partially correct?. I have been on a real health kick recently and am focusing on making sure I have plenty of fiber and protein in my diet. I have purchased the followi...

Please help me solve the problem. Thank you.. 3 The matrix A = has eigenvalue \1 # 2 with corresponding eigenvector N CO and 2 eigenvalue 12 = 1 with corresponding eigenvector Use this information to ...

Please I need help solving the problem. Thank you.. Find the eigenvalues and eigenvectors of the linear transformation T : P1 - P1 given by Tax + b) = (7a - 10b)x + (2a - 2b). Eigenvalue: 1 = 3 Eigenv...

Please I need help solving the problem. Thank you.. For a matrix A, the eigenvalues and a basis for the corresponding eigenspace are given below. Eigenvalue: 1 = 3 Eigenvalue: 1 = 2 5 1 2 9 12 8 Eigen...

Please I need help solving the problem. Thank you.. Complete the matrix representation for the linear transformation T: P2 -> P2 given by Tax' + ba + c) - (6a + 56 -3c)x2 + (3a + 46 + 4c)x + (3a + ...

. Show that 1 is an eigenvalue of A and find one eigenvector v corresponding to this eigenvalue. 9 1 -1 A = 1 7 1 , 1 = 8 4 2 6 V = Need Help? Read It Watch It. Find the eigenvalues and eigenvectors...

. Find the characteristic polynomial of the matrix, using either a cofactor expansion or the special formula for 3 x3 determinants. [Note: Finding the characteristic polynomial of a 3 x3 matrix is n...

. 2 -10 -2 Is V= 3 an eigenvector of A = 2 5 - 4 ? If so, find the eigenvalue. 2 0 2 -2 . . . Select the correct choice below and, if necessary, fill in the answer box within your choice. O A. Yes, ...

. Let W be the set of all vectors of the form shown on the right, where a, b, and c represent arbitrary real numbers. Find a set S of vectors that spans W or 3a + 4b give an example or an explanatio...

. < Question 1 of 20 This test: 20 point(s) possible This question: 1 point(s) possible Submit test Let V be the set of vectors shown below. a. If u and v are in V, is u + v in V? Why? b. Find a ...