Let b = {(1, 3), (−2, −2)} and b' = {(−12, 0), (−4, 4)} be bases for r2, and let a = 0 2 3 4 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' = [−2 4]t. [v]b = [t(v)]b =
(c) find p−1 and a' (the matrix for t relative to b'). p−1 = a' = (
(d) find [t(v)]b' two ways. [t(v)]b' = p−1[t(v)]b = [t(v)]b' = a'[v]b' =