If A= 1&1&-2 2&1&-3 5&4&-9 , find |A |. - Vidyadip

Question

If $\text{A}=\begin{bmatrix}1&1&-2\\2&1&-3\\5&4&-9\end{bmatrix},$ find $\left|\text{A}\right|.$

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Answer

$\text{Let A}=\begin{bmatrix}1&1&-2\\2&1&-3\\5&4&-9\end{bmatrix}.$
By expanding along the first row, we have:
$\left|\text{A}\right|=1\begin{vmatrix}1&-3\\4&-9\end{vmatrix}-1\begin{vmatrix}2&-3\\5&-9\end{vmatrix}-2\begin{vmatrix}2&1\\5&4\end{vmatrix}$
$=1(-9+12)-1(-18+15)-2(8-5)$
$ =1(3)-1(-3)-2(3)$
$ =3+3-6$
$=6-6$
$=0$

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