T U V and S V W are linear transformations and B, C, and D are bases for U, V, and W, respectively Compute S T DB in two ways (a) by finding S T directly and then computing its matrix and (b) by finding the matrices of S and T separately and using Theorem 6 27 T P 1 P 2 defined by T(p(x)) p(x 1), S...

T : U V and S : V W are linear transformations and B, C,

Question:

T : U → V and S : V → W are linear transformations and B, C, and D are bases for U, V, and W, respectively. Compute [S ͦ T]_D←Bin two ways: (a) by finding S ͦ T directly and then computing its matrix and (b) by finding the matrices of S and T separately and using Theorem 6.27.

T : P₁ → P₂ defined by T(p(x)) = p(x + 1),
S : P₂ → P₂ defined by S(p(x)) = p(x + 1),
B = {1, x}, C = D = {1, x, x²}