If $A = \begin{bmatrix} 3 & 2 & 4 \ 1 & 2 & 1 \ 3 & 2 & 6 \end{bmatrix}$and$\ A_{ij}$are the cofactors of $a_{ij}$, then $a_{11}A_{11} + a_{12}A + a_{13}A_{13}$is equal to

Question

Dr. Abubacker · Accepted Answer

(a)
$a_{11}A_{11} + a_{12}A_{12} + a_{13}A_{13}$
$= 3\left| \begin{array}{r}
2\ \ \ 1 \
2\ \ \ 6
\end{array} ight| - 2\left| \begin{array}{r}
1\ \ 1 \
3\ \ 6
\end{array} ight| + 4\left| \begin{array}{r}
1\ \ 2 \
3\ \ 2
\end{array} ight|$
=$3(12 - 2) - 2(6 - 3) + 4(2 - 6)$
$= 30 - 6 - 16 = 8$

Q. If $A = \begin{bmatrix} 3 & 2 & 4 \\ 1 & 2 & 1 \\ 3 & 2 & 6 \end{bmatrix}$and$\ A_{ij}$are the cofactors of $a_{ij}$, then $a_{11}A_{11} + a_{12}A + a_{13}A_{13}$is equal to

Explanation

Reviewed by Dr. Abubacker

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