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Evaluate $$\left| {\begin{array}{*{20}{c}} 0&1&2 \\ { - 1}&0&{ - 3} \\ { - 2}&3&0 \end{array}} \right|$$
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## QuestionMathsClass 12

Evaluate $$\left| {\begin{array}{*{20}{c}} 0&1&2 \\ { - 1}&0&{ - 3} \\ { - 2}&3&0 \end{array}} \right|$$

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