Consider a matrix A = |2 6 3 4| It is required to find its inverse.

Question

Consider a matrix
[latex]\overline{A}=\left|\begin{matrix} 2&6 \ 3&4 \end{matrix} ight| [/latex]
It is required to find its inverse.

Accepted Answer

Attach a unit matrix of 2 × 2 and perform the operations as shown as follows:

[latex]\left|\begin{matrix} 2&6 \ 3&4 \end{matrix} ight| \left|\begin{matrix} 1&0 \ 0&1 \end{matrix} ight| → \frac{R_{1}}{2} \left|\begin{matrix} 1&3 \ 3&4 \end{matrix} ight|\left|\begin{matrix} \frac{1}{2}&0 \ 0&1 \end{matrix} ight| → R_{2} \ - \ 3R_{1} \left|\begin{matrix} 1&3 \ 0&-5 \end{matrix} ight|\left|\begin{matrix} \frac{1}{2}&0 \\ \frac{-3}{2}&1 \end{matrix} ight|→ R_{1}+ \frac{5}{3}R_{2}[/latex]

[latex]\left|\begin{matrix} 1&0 \ 0&-5 \end{matrix} ight|\left|\begin{matrix} \frac{-2}{5} & \frac{3}{5} \\ \frac{-3}{2}&1 \end{matrix} ight|→ R_{2} \ - \frac{1}{5}\left|\begin{matrix} 1&0 \ 0&1 \end{matrix} ight| \left|\begin{matrix} \frac{-2}{5} & \frac{3}{5} \\ \frac{3}{10}& \frac{-1}{5} \end{matrix} ight|[/latex]

Thus, the inverse is
[latex]\overline{A}^{-1}= \left|\begin{matrix} \frac{-2}{5} & \frac{3}{5} \\ \frac{3}{10}&\frac{-1}{5} \end{matrix} ight|[/latex]

Question A.5: Consider a matrix A = |2 6 3 4| It is required to find its i......

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