Please provide specific explanations with each correct answers. Thanks.
(a). Let A = [B|U] =
1 |
-1 |
-1 |
1 |
1 |
1 |
1 |
1 |
0 |
-1 |
1 |
0 |
1 |
0 |
1 |
-1 |
0 |
1 |
The RREF of A is
1 |
0 |
0 |
-1/3 |
2/3 |
2/3 |
0 |
1 |
0 |
-2/3 |
1/3 |
-2/3 |
0 |
0 |
1 |
-2/3 |
-2/3 |
1/3 |
Hence the change of coordinate matrix from the basis U to the basis B is M (say) =
-1/3 |
2/3 |
2/3 |
-2/3 |
1/3 |
-2/3 |
-2/3 |
-2/3 |
1/3 |
(b). The change of coordinate matrix from the basis B to the basis U is M-1 =
-1/3 |
-2/3 |
-2/3 |
2/3 |
1/3 |
-2/3 |
2/3 |
-2/3 |
1/3 |
so that [x]U = M-1[x]B = (-7/3,2/3,-1/3)T.
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