Suppose T is a linear transformation between vector spaces V and W, with corresponding bases B = {v1, V2, V3 }, C = {w1, w2, w3} Suppose too that T(v1) = w1 + w2 + w3 and T(v2) = w2 + w3 and T(v3) = w3 A. Find the matrix A for T relative to these bases. B. What input vector v satisfies T(v) = w1? C. Find the inverse matrix. D. Find T-1(w1), T-'(w2), T-1(w3)

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
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Suppose T is a linear transformation between vector spaces V and W, with corresponding bases B = {v1, V2, V3}, C = {w1, W2, W3}
Suppose too that
T(v1)
= w1 + w2 + w3 and
T(v2)
W2 + w3
and
T(v3)
= W3
A. Find the matrix A for T relative to these bases.
B. What input vector v satisfies T(v)
w1?
C. Find the inverse matrix.
D. Find T- (w1), T-'(w2), T(w3)
Transcribed Image Text:Suppose T is a linear transformation between vector spaces V and W, with corresponding bases B = {v1, V2, V3}, C = {w1, W2, W3} Suppose too that T(v1) = w1 + w2 + w3 and T(v2) W2 + w3 and T(v3) = W3 A. Find the matrix A for T relative to these bases. B. What input vector v satisfies T(v) w1? C. Find the inverse matrix. D. Find T- (w1), T-'(w2), T(w3)
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