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 ] ⇒ [((1 2)),((0 1)) ]= [(( 1 0)),(((2/5) −(1/5))) ].A [R_2 →(−(1/5))R_2 ] ⇒ [((1 0)),((0 1)) ]= [(((1/5) (2/5))),(((2/5) −(1/5))) ].A [R_1 →R_1 −2R


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

$2 . [\begin{matrix} 1 2 \\ 2 - 1 \end{matrix}]$ $S o l n : [\begin{matrix} 1 2 \\ 2 - 1 \end{matrix}] = [\begin{matrix} 1 0 \\ 0 1 \end{matrix}] . A$ $\Rightarrow [\begin{matrix} 1 2 \\ 0 - 5 \end{matrix}] = [\begin{matrix} 1 0 \\ - 2 1 \end{matrix}] . A [R_{2} \to R_{2} - 2 R_{1}]$ $\Rightarrow [\begin{matrix} 1 2 \\ 0 1 \end{matrix}] = [\begin{matrix} 1 0 \\ \frac{2}{5} - \frac{1}{5} \end{matrix}] . A [R_{2} \to (- \frac{1}{5}) R_{2}]$ $\Rightarrow [\begin{matrix} 1 0 \\ 0 1 \end{matrix}] = [\begin{matrix} \frac{1}{5} \frac{2}{5} \\ \frac{2}{5} - \frac{1}{5} \end{matrix}] . A [R_{1} \to R_{1} - 2 R_{2}]$ $∴ A^{- 1} = \frac{1}{5} [\begin{matrix} 1 2 \\ 2 - 1 \end{matrix}]$
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