Question

5:52 .11 LTE . a webassign.net Use a software program or a graphing utility to find the transition matrix from B to B", find the transition matrix from B' to B, venify that the two transition matrices are inverses of each other, and find the coordinate matrix xls. given the coordinate matrix (xs (a) Find the transition matrix from B to B (b) Find the transition matrix from B' to B (c) Verify that the two transition matrices are inverses of each other (d) Find the coordinate matrix [xls. given the coordinate matrix [xle- Use a software program or a graphing utility to find the transition matrix from B to B", find the transition matrix from B' to B, venity that the two 5:52 LTED webassign.net a rina tne cooroinate maxxl given the coorainate matrx xe Use a software program or a graphing utility to find the transition matrix from B to B', find the transition matrix from B'to B, venify that the two transition matrices are inverses of each other, and find the coordinate matrix [xls. given the coordinate matrix [xs (a) Find the transition matrix from B to B (b) Find the transition matrix from B' to B. (c) Verify that the two transition matrices are inverses of each other (d) Find the coordinate matrix [xls. given the coordinate matrix [xa- a 回 5:52 .11 LTE . a webassign.net Use a software program or a graphing utility to find the transition matrix from B to B", find the transition matrix from B' to B, venify that the two transition matrices are inverses of each other, and find the coordinate matrix xls. given the coordinate matrix (xs (a) Find the transition matrix from B to B (b) Find the transition matrix from B' to B (c) Verify that the two transition matrices are inverses of each other (d) Find the coordinate matrix [xls. given the coordinate matrix [xle- Use a software program or a graphing utility to find the transition matrix from B to B", find the transition matrix from B' to B, venity that the two 13. 1/4 points I Previous Answers LarLinAlg8 4.7.041 My Notes Ask Your Teacher Use a software program or a graphing utility to find the transition matrix from B to B', find the transition matrix from B' to B, verify that the two transition matrices are inverses of each other, and find the coordinate matrix [x]B, given the coordinate matrix [x]B B-((100,-2,-4),-40, 1, 2),(120,-3,-5) (xl 1 -1 2

Answer 1

151/13 -138/13 284/1329/32 69/32 -65/16 (c)PP-345/13-332/13 671/13 445/64 133/64 -257/32 -220/13-207/13 839/26 125/32 69/32 -97/16 -o 101 -151/13 -138/13 284/13 -1 719/13 d)Now"|&јв=PB-BkļR'-1-345 / 13-332/13 67 1 / 13|| 0-168 7 / 13 L-220/13-207 / 13 839 / 26L2J L1059/13]

(13)Given B- (4,2,-4), (6,-5,-6),(2,-18) B'= {(100,-2-4),(-40, 1,2),(-120,-3,-5) a First find the change of basis matrix from B to B express each vector of B as a linear combination of vectors of B Find 2 100 -40 -120 4-100a- 406-120c 21 solving, we get (a=-,b=-_c = 4 21/5 Then, | 2 | -|-68/5 -8 Find -5 100 120 6 100a-40b-120c 97118 solving, we get -97/10 Then,51185 16 Find-1 100 -120 2 100a-40b-120c -1--2a+b-3c 8=-4a + 2b-5c 19 126 la solving, wepet b=-.c=10 10 -19/10 Then,12/5 10 21/5 -97/10-19/10 So, the change ofbasis matrix is P-68/5 118/5 126/5 16 10

(b)First find the change of basis matrix from B to B express each vector of B' as a linear combination of vectors of B 100 Find -2 100 4 6 100 4a+6b+2c -2-2a-5b-c -4--4a-6b +8c 281 4 48 20 10 5 281/20 Then,-241/10 48/5 100 Find1 -40 -40 4a 6b+2c 1= 2a-5b-c 447 67 19 solving, we get,a_-_,b_-_.c=- -447/80 Then, 167/40 B L19/5 120 Find -3 120 4 120 = 4a + 6b+2c 3-2a-5b-c 67 soving, we getab-5 1201 Γ67 / 4 Then, -35 23/2 281/20-447/80 67/4 So, the change of basis matrix is P41/10 -67/405 48/5-19/5 23/2