Question

In the following matrix equation use elementary operation R₂ → R₂ + R₁ and the equation thus obtained:

$\left[\begin{array}{cc}2& 3\\ 1& 4\end{array}\right]\left[\begin{array}{cc}1& 0\\ 2& -1\end{array}\right]=\left[\begin{array}{cc}8& -3\\ 9& -4\end{array}\right]$

Answer 1

$\left[\begin{array}{cc}2& 3\\ 1& 4\end{array}\right]\left[\begin{array}{cc}1& 0\\ 2& -1\end{array}\right]=\left[\begin{array}{cc}8& -3\\ 9& -4\end{array}\right]$

By applying elementary operation R₂ → R₂ + R₁, we get

$\left[\begin{array}{cc}2& 3\\ 3& 7\end{array}\right]\left[\begin{array}{cc}1& 0\\ 2& -1\end{array}\right]=\left[\begin{array}{cc}8& -3\\ 17& -7\end{array}\right]$ (Every row operation is equivalent to left-multiplication by an elementary matrix.)