1 0 04 5 6 Matrix A-LR, L16 1 0, R 0 21 LY b, b2 Find the value of y3
6. 0/1 points | Previous Answers HoltLinAlg2 4.4.023 Find the change of basis matrix from B2 to B 2 B153 817 7 2 8 eBook 6. 0/1 points | Previous Answers HoltLinAlg2 4.4.023 Find the change of basis matrix from B2 to B 2 B153 817 7 2 8 eBook
QUESTION # 04 Consider the matrix A= 0 5 1-6 -6 -11 9 4 -6 4 Find all eigenvalues of A Find the eigenvectors of A Can we diagonalize A? If no why? If yes then diagonalize A.
Exercise 5 Let 2 1 -2 -1 (a) Find A4 (b) Find eA (c) Find a matrix B such that B2 = A. Exercise 5 Let 2 1 -2 -1 (a) Find A4 (b) Find eA (c) Find a matrix B such that B2 = A.
Tk 1 21 5 -5 k (a) Find the determinant of A in terms of k (b) For which value(s) of k is the matrix A invertible? (c) Let B-(k,1,2,0), (0, k, 2,0),(5,-5, k,0)) be a set of vectors in R4, and let k equal some answer you gave for part (b) of this question. Add an appropriate number of vectors to B so that the resulting set is a basis for R' Tk 1 21 5 -5 k (a)...
6. Find the matrix P that projects vectors in R4 onto the column space of each matrix. 2 1 [BB]A= 1-21 0 1 (b) A= | 0 1 1 -1 (a) 1131 0101 1011 1231 1112 6. Find the matrix P that projects vectors in R4 onto the column space of each matrix. 2 1 [BB]A= 1-21 0 1 (b) A= | 0 1 1 -1 (a) 1131 0101 1011 1231 1112
Assume that the transition matrix from basis B = {b1, b2, b3} to basis C = {c1, c2, c3} is PC,B = 1/2*[ 0 -1 1 ; -1 1 1 ; 1 0 0 ]. (a) If u = b1 + b2 + 2b3, find [u]C. (b) Calculate PB,C. (c) Suppose that c1 = (1, 2, 3), c2 = (1, 2, 0), c3 = (1, 0, 0) and let S be the standard basis for R 3 . (i) Find...
0 0 Q2. Consider the matrix A 6 2 -5 0 1 (a) Find all eigenvalues of the matrix A. (7 pts) (b) Find all eigenvectors of the matrix A. (8 pts) (c) Do you think that the set of the eigenvectors of A is a basis for the vector space R*? (Justify your answer) (5 pts)
3. (6 marks) For b1,b2, 63, 64 € R, consider the linear system of equations + 21 + 22 -11 + 22 23 624 = bi 3.13 + 2014 b2 23 + 2:04 b3 603 + 20:24 = 54 *) 21 + 2:01 + 4.22 where 11, 12, 13, 14 ER. (a) Find a system of equations that bı, b2, 63, 64 must satisfy in order for (+) to be consistent. bi [ must satisfy so (+) is (b) Using...
Find an SVD of the matrix. 6-5 A= 0-6 Find an SVD of the matrix. 6-5 A= 0-6
Problem 3 1. Prove that B (51, b2, b3,-4} {а, ег#3+ега, +6) is the basis for R4. al 2. Find 1 4 0 0 0 : 0 0 0 00 0 b 3. Consider the map T: R4-W with B-matrix B a 。), Find the standard matrix 1896 of T Problem 3 1. Prove that B (51, b2, b3,-4} {а, ег#3+ега, +6) is the basis for R4. al 2. Find 1 4 0 0 0 : 0 0 0 00...