Evaluate 5&4&3 3&4&1 5&6&1 is: 1. 4 2. -24 3. -8 4. 8 - Vidyadip

Question

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

4
-24
-8
8

✓

Answer

-8

Solution:

Expanding along the first row, we get

$\triangle=5\begin{bmatrix}4&1\\6&1\end{bmatrix}-4\begin{bmatrix}3&1\\5&1\end{bmatrix}+3\begin{bmatrix}3&4\\5&6\end{bmatrix}$

$=5(4-6)-4(3-5)+3(18-20)$

$=5(-2)-4(-2)+3(-2)=-10+8-6=-8.$

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