Question

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

Answer 1

A= $$\left[\begin{array}{cc}1& -1\\ 2& 3\end{array}\right]$$ Coverting into Identity matrix $$\left[\begin{array}{cc}1& 0\\ 0& 1\end{array}\right]$$ $R_2\to R_2-2R_1$ $$\left[\begin{array}{cc}1& -1\\ 2-2\left(1\right)& 3-2(-1)\end{array}\right]$$ $$\left[\begin{array}{cc}1& -1\\ 0& 5\end{array}\right]$$ $R_2\to \frac{R_2}{5}$ $$\left[\begin{array}{cc}1& -1\\ 0& \frac{5}{5}\end{array}\right]$$ $$\left[\begin{array}{cc}1& -1\\ 0& 1\end{array}\right]$$ Now, $R_1\to R_1+R_2$ $$\left[\begin{array}{cc}1+0& -1+1\\ 0& 1\end{array}\right]$$ $$\left[\begin{array}{cc}1& 0\\ 0& 1\end{array}\right]$$