Question

covert it into an upper triangular matrix
Convert $\left[\begin{array}{c}1\\ 2\end{array}\begin{array}{c}-1\\ 3\end{array}\right]$ into an identity matrix by suitable row transformations.

Answer 1

$\left|\begin{array}{cc}1& -1\\ 2& 3\end{array}\right|$

$R_2\to R_2-2R_1$

$\left|\begin{array}{cc}1& -1\\ 0& 5\end{array}\right|$

upper triangular matrix.

For convert identity matrix

$\Rightarrow R_1\to R_1+\frac{R_2}{5}$

$\left[\begin{array}{cc}1& 0\\ 0& 5\end{array}\right]$

$R_2\to \frac{R_2}{5}$

$\Rightarrow \left[\begin{array}{cc}1& 0\\ 0& 1\end{array}\right]$

Identity matrix