I The linear transformation T: R R. T(2) Ar, is defined by the matrix A relative to the standard basis B={,2,3}: [102] A=0 3 0 - 201 4. Show that D = PT AP = 8. 1. Find the eigenvalues () for A. 2. Find the set of orthornormal eigenvectors {p}. 3. Show that the P = P P2 P3] is symmetric, i.e. PT = P-1 A 0 0 0 1 0. 0 0 5. Bonus. Show that pi Api = X 2 = B -8. 6. D is the matrix for T with respect to the eigenbasis B'={p.P2, P3). i. Is P from 3. the transition matrix from B' to B? Hint: Does [B' B] [I P-1] produce the same P? III Find the orthogonal compliment to S 23 = ii. What do each of the eigenvectors look like with respect to the eigenbasis? Hint: P = PPB. II Using the vectors =(-1,0,1) and = (0, 1.0) solve the following problems 1. 5-40 5. x 2. d(50, 40) 6. 3. (5)-(40) 4. proje 7. span{ x+x (-proj #) WMAT-291, section W1, xbhcc moodle - Bing X 2021SP MAT-291-W1: X > C File | C:/Users/youssef/Downloads/MAT291_Final_SP21.pdf 2 A of 2 Q Type here to search + (0) IV The matrix A = A = Find the kernal and range (row space) of T. O Using A= PDF V Using any method covered this semester, solve the system Az= b using the following matrices: 1 0 5 0 6= 8 -2 1 4 < A, B >= aobo + ab +2a2b2 +3a3b3. 1 0 -2 0 5 0 defines the linear transformation T:R R, T(7) = Az. -2 1 4 VI An inner product for M2,2 matrices {4=[90], ao, a1, 02, 03 R} is defined as 02 03 2 [13] CD Page view A Read aloud | Draw MAT291_Final_SP21.pc X 6: and B= 3. Calculate || B||. 4. Calculate < A,B>. 1. Calculate the determinant [2B|. 2. Calculate ||A|| = . course hero - Bing answer the following questions. 5. Calculate the angle between A and B. 6. List one isomorphic vector space to M,2- V X Course Hero Highlight Q x + Erase 0 [+] A P 60 x 4x J 10 12:09 PM 5/16/2021