Question

Question 7. For the matrix A and ordered basis B, find LAB (using the definition of matrix representation). Also, find an invertible matrix Q such that [LA]g = Q-'AQ. (Note: you do NOT need to find Q-'). (2 1 1 A = 3 -1 0 , B= 1 -1 11 1 1) 10) 1 --03:9--20:00

Answer 1

Solve we have 2 1 1 4633-6 0-3) 3-10 N na Let a,b and c be the scalars such that -(1) - () - +49-6-16) a 1 + b 2 - 1 tc a + 2b + 36 1 a-b+2c 1. btc - On comparing we get a + 2b + 36 - 3 a-6 +26 = 2 and b + c = 2 On solving, We get a = -7/ , b = -1 // , c = 2

similarly let 19 TL 10 1 - t 1 mn- = Q = -9%, b= -5/2 , C=91, . Also -* (0) = 6) = 465-- tel = a=-11,b=-2, C= 8 Therefore -72 [lae = 1 -912 - 1/2 -5/2-2 1572 92 0

having ordered We know that Q is just a matrix basis vutors as its columns. Q=1' 231 . We can easily verify that Thale = Q-AQ. Here Q-AQ 1 / -1/2 1/2 le % -1% -12 112 Illi 231 Yo -112 - 12 | 13-10|?-12 1-2 12 312 111 1011 1-1/2 -5/2-2) = ILAJE 15/2 9/ 28 Thus our answer is corret.
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