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{\bf Question}

Write down the matrix of the minors $M_{ij}$ and the matrix of
cofactors $A_{ij} $ associated with the matrix $A= \left(
\begin{array}{ccc} 1 &amp; 2 &amp; 3 \\ 4 &amp; 5 &amp; 6 \\ 1 &amp; 1 &amp; 1
\end{array} \right)$ with elements $a_{ij}$

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{\bf Answer}

$A= \left( \begin{array}{ccc} 1 &amp; 2 &amp; 3 \\ 4 &amp; 5 &amp; 6 \\ 1 &amp; 1 &amp; 1
\end{array} \right)$

Minors
\begin{eqnarray*} [M_{ij}] &amp; = &amp; \left[ \begin{array}{ccc}
\left|\begin{array}{cc} 5 &amp; 6 \\ 1 &amp; 1 \end{array}\right| &amp;
\left|\begin{array}{cc} 4 &amp; 6 \\ 1 &amp; 1 \end{array}\right| &amp;
\left|\begin{array}{cc} 4 &amp; 5 \\ 1 &amp; 1 \end{array}\right| \\ \\
\left|\begin{array}{cc} 2 &amp; 3 \\ 1 &amp; 1 \end{array}\right| &amp;
\left|\begin{array}{cc} 1 &amp; 3 \\ 1 &amp; 1 \end{array}\right| &amp;
\left|\begin{array}{cc} 1 &amp; 2 \\ 1 &amp; 1 \end{array}\right| \\ \\
\left|\begin{array}{cc} 2 &amp; 3 \\ 5 &amp; 6 \end{array}\right| &amp;
\left|\begin{array}{cc} 1 &amp; 3 \\ 4 &amp; 6 \end{array}\right| &amp;
\left|\begin{array}{cc} 1 &amp; 2 \\ 4 &amp; 5 \end{array}\right| \\
\end{array}\right]\\ &amp; = &amp; \left( \begin{array}{ccc} -1 &amp; -2 &amp; -1 \\
 -1 &amp; -2 &amp; -1 \\ -3 &amp; -6 &amp; -3\end{array} \right) \end{eqnarray*}

Cofactors

$[A_{ij}] =  \left( \begin{array}{ccc} -1 &amp; 2 &amp; -1
\\  1 &amp; -2 &amp; 1 \\ -3 &amp; 6 &amp; -3\end{array} \right)$



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