Find the matrix A’ for T relative to the basis B’. T: R2 + R2, T(x,…
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Question “Find the matrix A’ for T relative to the basis B’. T: R2 + R2, T(x,…”
Find the matrix A’ for T relative to the basis B’. T: R2 + R2, T(x, y) = (3x – y, 4x), B’ = {(-2, 1), (-1, 1)} A’ =
Let B = {(1, 3), (-2,-2)} and B’ = {(-12, 0), (-4,4)} be bases for R2, and let 0 2 A = 3 4 be the matrix for T: R2 + R2 relative to B. (a) Find the transition matrix P from B’ to B. 6 4 P= 9 4 (b) Use the matrices P and A to find [v]g and [T(v)]B, where [v]B’ = [-2 5] [v] [T(v)]B (c) Find p-1 and A’ (the matrix for I relative to B’). P-1 = A=
(d) Find [T(v)]B’ two ways. [T(v)]g’ = p-1[T(v)]B [T(v)]B’ = A'[v]B’
Answer
Which matrix is required for T relative to B’?
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T(2, y) = (5.r – y, 4.1)
B’ = (-2,1),(-1,1)
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– 5.r – y = (-2) + (-1)02: 4.c = c + c
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C2 = 4.0 – (-9.2 + y)
C2 13.C – Y
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T(2, y) = (-9.r + y) (-2,1) + (13.1 – y) (-1,1)
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197-2.11-27(-1.1)
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Conclusion
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