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Concept:
Let A = \(\rm \begin{vmatrix} a_{1} & a_{2} & a_{3}\\ b_{1} & b_{2} & b_{3}\\ c_{1} & c_{2} & c_{3} \end{vmatrix}\)
det(A) = a 1 (b 2 c3 - b 3 c 2) - a 2 (b 1 c3 - b 3 c 1) + a 3 (b 1 c2 - b 2 c1 )
Calculation:
Given:
\(f(-1) = \rm \left| {\begin{array}{*{20}{c}} 1&-1&{0}\\ {-2}&{{2}}&{0}\\ {6}&{12}&0 \end{array}} \right|= 1(0 - 0) + 1(0 - 0) + 0(-24 - 12) = 0\)
\(f(0) = \rm \left| {\begin{array}{*{20}{c}} 1&0&{1}\\ {0}&{{0}}&{0}\\ {0}&{4}&0 \end{array}} \right|= 1(0 - 0) - 0(0 - 0) + 1(0 - 0) = 0\)
\(f(1) = \rm \left| {\begin{array}{*{20}{c}} 1&1&{2}\\ {2}&{{0}}&{2}\\ {0}&{0}&0 \end{array}} \right| = 1(0 - 0) -1(0 - 0) + 2(0 - 0) = 0\)
Now;
f(-1) + f(0) + f(1) = 0
Similar Questions
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Important Questions from Evaluation of Determinants
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