Exercise 2

Consider a linear map $f\colon V\to W$ represented with respect to some bases $B,D$ by the matrix. Decide if that map is nonsingular.

• (a)  $\begin{pmatrix}2&1\\ 3&4\end{pmatrix}$     (b)  $\begin{pmatrix}1&1\\ -3&-3\end{pmatrix}$     (c)  $\begin{pmatrix}3&0&0\\ 2&1&0\\ 4&4&4\end{pmatrix}$     (d)  $\begin{pmatrix}2&0&-2\\ 1&1&0\\ 4&1&-4\end{pmatrix}$