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Let B = {(1, 2), (−1, −1)} and B' = {(−4, 1), (0, 2)} be bases...

Let B = {(1, 2), (−1, −1)} and B' = {(−4, 1), (0, 2)} be bases for R2, and let A = −1 2 1 0 be the matrix for T: R2 → R2 relative to B. (a) Find the transition matrix P from B' to B. P =

(b) Use the matrices P and A to find [v]B and [T(v)]B , where [v]B' = [−3 1]T. [v]B = [T(v)]B =

(c) Find P inverse−1 and A' (the matrix for T relative to B'). P−1 = A' =

(d) Find [T(v)]B' two ways.

[T(v)]B' = P inverse1[T(v)]B =

[T(v)]B' = A'[v]B' =

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