Evaluate 3&-1&3 6&-5&4 3&-2&3 is: - Vidyadip

MCQ

Evaluate $\begin{bmatrix}3&-1&3\\6&-5&4\\3&-2&3\end{bmatrix}$ is:

A
$100$
B
$223$
✓
$240$
D
$230$

✓

Answer

Correct option: C.

$240$

Expanding along $\text{R}_1,$ we get
$\triangle=\begin{bmatrix}3&-1&3\\6&-5&4\\3&-2&3\end{bmatrix}$
$\triangle=3\begin{bmatrix}-5&45\\-2&3\end{bmatrix}-(-1)\begin{bmatrix}6&4\\3&3\end{bmatrix}+3\begin{bmatrix}6&-5\\-3&-2\end{bmatrix}$
$\triangle=3(-15+90)+(18-12)+3(-12+15) $
$\triangle=3(75)+6+9=240. $

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