Question

Convert $\left[\begin{array}{cc}1& -1\\ 2& 3\end{array}\right]$ into an identity matrix by suitable row transformations.

Answer 1

Given Matrix $A=\left[\begin{array}{cc}1& -1\\ 2& 3\end{array}\right]$

Applying $R_2\to R_2-2R_1$

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

$R_2\to \frac{1}{5}{R}_2$

$A\sim \left[\begin{array}{cc}1& -1\\ 0& 1\end{array}\right]$

$R_1\to R_1+R_2$

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