Evaluate: | ccc 2 & -5 & 7 5 & 2 & 1 9 & 0 & 2 | - Vidyadip

Question

Evaluate:

$\left|\begin{array}{ccc}2 & -5 & 7 \\ 5 & 2 & 1 \\ 9 & 0 & 2\end{array}\right|$

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Answer

$\left|\begin{array}{ccc}2 & -5 & 7 \\ 5 & 2 & 1 \\ 9 & 0 & 2\end{array}\right|$

$\left|\begin{array}{ccc}2 & -5 & 7 \\ 5 & 2 & 1 \\ 9 & 0 & 2\end{array}\right|=2\left|\begin{array}{ll}2 & 1 \\ 0 & 2\end{array}\right|-(-5)\left|\begin{array}{ll}5 & 1 \\ 9 & 2\end{array}\right|+7\left|\begin{array}{ll}5 & 2 \\ 9 & 0\end{array}\right|$

= 2(4 – 0) + 5(10 – 9) + 7(0 – 18) = 2(4) + 5(1) + 7(-18) = 8 + 5 – 126 = -113

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