Due Wednesday, October 2, in class

Section 2.2 problems 1, 4, 14, 15, 16
Section 2.3 problems 1, 3, 10, 16

Then

A. Let \(V,W\) be vector spaces over \(F\) with ordered bases \(\beta = \{v_1,\ldots, v_n\}\) and \(\gamma = \{ w_1,\ldots, w_m\}\), respectively. Show that the function \(G:\ \mathcal{L}(V,W) \to M_{m\times n}(F)\) given by \(G(T) = [T]_\beta^\gamma\) is a linear transformation. (Side note: \(G\) is an element of \(\mathcal{L}(\mathcal{L}(V,W), M_{m\times n}(F)).\)