2-1-2-2-1-Soln-1-2-2-1-1-0-0-1-A-1-2-0-5-1-0-2-1-A-R-2-R-2-2R-1

Question Number 170022 by Moytea last updated on 14/May/22

2 . [\begin{matrix} 1 2 \\ 2 - 1 \end{matrix}]

S o l n : [\begin{matrix} 1 2 \\ 2 - 1 \end{matrix}] = [\begin{matrix} 1 0 \\ 0 1 \end{matrix}] . A

\Rightarrow [\begin{matrix} 1 2 \\ 0 - 5 \end{matrix}] = [\begin{matrix} 1 0 \\ - 2 1 \end{matrix}] . A [R_{2} \to R_{2} - 2 R_{1}]

\Rightarrow [\begin{matrix} 1 2 \\ 0 1 \end{matrix}] = [\begin{matrix} 1 0 \\ \frac{2}{5} - \frac{1}{5} \end{matrix}] . A [R_{2} \to (- \frac{1}{5}) R_{2}]

\Rightarrow [\begin{matrix} 1 0 \\ 0 1 \end{matrix}] = [\begin{matrix} \frac{1}{5} \frac{2}{5} \\ \frac{2}{5} - \frac{1}{5} \end{matrix}] . A [R_{1} \to R_{1} - 2 R_{2}]

∴ A^{- 1} = \frac{1}{5} [\begin{matrix} 1 2 \\ 2 - 1 \end{matrix}]