Question

Let A and B be two ordered bases of V, and consider a linear transformation T: V → V. Suppose that the change of base matrix [T]B to [T]A is given by

Answer 1

The question is about linear transformations and change of base matrices in the context of vector spaces.

Step-by-step explanation:

The given question is about linear transformations and change of base matrices in the context of vector spaces. Let A and B be two ordered bases of V, and T be a linear transformation from V to V. The change of base matrix [T]B to [T]A represents the transformation T in the basis A using the basis B. The matrix elements [T]B to [T]A can be found by expressing the vectors in terms of their vector component forms and performing the necessary calculations.