We were unable to transcribe this image
We were unable to transcribe this image
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