Exercise 4

Decide if each vector lies in the range of the map from $\mathbb{R}^{3}$ to $\mathbb{R}^{2}$ represented with respect to the standard bases by the matrix.

• (a)  $\begin{pmatrix}1&1&3\\ 0&1&4\end{pmatrix}$, $\begin{pmatrix}1\\ 3\end{pmatrix}$     (b)  $\begin{pmatrix}2&0&3\\ 4&0&6\end{pmatrix}$, $\begin{pmatrix}1\\ 1\end{pmatrix}$