Exercise 2

Predict the result of each multiplication by an elementary reduction matrix, and then check by multiplying it out.

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