(1 point) In the following, B = {(1,0), (0, 1)} and B\' = { ui , u2 } . For each
ID: 3116882 • Letter: #
Question
(1 point) In the following, B = {(1,0), (0, 1)} and B' = { ui , u2 } . For each of the following, find the transition matrix corresponding to the change in basis from B' to B. (B is the standard basis for R2) (a) ui = (1,1), u2 = (1,2) Transition matrix: (b) ui = (2, 7), u2 = (1 , 4) Transition matrix: (c) u i = (-1, 1), u2 = (2, 2) Transition matrix: For each of the ordered bases B' = , u2 } in the previous part of this problem, find the transition matrix corresponding to the change in basis from B to B'. (B is the standard basis for R2)Explanation / Answer
(a). B is the standard matrix for R2. The transition matrix for the change of base from B’ to B is
1
1
1
2
(b). The transition matrix for the change of base from B’ to B is
2
1
7
4
(c ). The transition matrix for the change of base from B’ to B is
-1
2
1
2
1.Let A1 =
1
1
1
0
1
2
0
1
The RREF of A1 is
1
0
2
-1
0
1
-1
1
Therefore, the transition matrix for the change of base from B to B’ is
2
-1
-1
1
2.Let A2 =
2
1
1
0
7
4
0
1
The RREF of A2 is
1
0
4
-1
0
1
-7
2
Therefore, the transition matrix for the change of base from B to B’ is
4
-1
-7
2
3. Let A3 =
-1
2
1
0
1
2
0
1
The RREF of A3is
1
0
-1/2
1/2
0
1
1/4
1/4
Therefore, the transition matrix for the change of base from B to B’ is
-1/2
1/2
1/4
1/4
1
1
1
2
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