Evaluate: | ccc 1 & -3 & 12 0 & 2 & -4 9 & 7 & 2 | - Vidyadip

Question

Evaluate: $\left|\begin{array}{ccc}1 & -3 & 12 \\ 0 & 2 & -4 \\ 9 & 7 & 2\end{array}\right|$

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Answer

$\begin{aligned} & \left|\begin{array}{ccc}1 & -3 & 12 \\ 0 & 2 & -4 \\ 9 & 7 & 2\end{array}\right| \text { } \\ & =1\left|\begin{array}{rr}2 & -4 \\ 7 & 2\end{array}\right|-(-3)\left|\begin{array}{rr}0 & -4 \\ 9 & 2\end{array}\right|+12\left|\begin{array}{ll}0 & 2 \\ 9 & 7\end{array}\right| \\ & =1(4+28)+3(0+36)+12(0-18) \\ & =1(32)+3(36)+12(-18) \\ & =32+108-216 \\ & =-76\end{aligned}$

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