Evaluate the determinant | ccc 0 & 1 & 2 -1 & 0 & -3 -2 & 3 & 0 | - Vidyadip

Question

Evaluate the determinant $\left|\begin{array}{ccc}0 & 1 & 2 \\ -1 & 0 & -3 \\ -2 & 3 & 0\end{array}\right|$

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Answer

Given: $\left| {\begin{array}{*{20}{c}} 0&1&2 \\ { - 1}&0&{ - 3} \\ { - 2}&3&0 \end{array}} \right|$
Expanding along first row, $0\left| {\begin{array}{*{20}{c}} 0&{ - 3} \\ 3&0 \end{array}} \right| - 1\left| {\begin{array}{*{20}{c}} { - 1}&{ - 3} \\ { - 2}&0 \end{array}} \right| + 2\left| {\begin{array}{*{20}{c}} { - 1}&0 \\ { - 2}&3 \end{array}} \right|$
= 0(0 + 9) - (0 - 6) + 2( - 3 - 0)
= 0 + 6 - 6 = 0

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