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If the product of eigenvalues of the matrix \(A =\left[ {\begin{array}{*{20}{c}} {1}&{2}&{-1}\\ {3}&{5}&{2}\\ {1}&{k}&{2} \end{array}} \right]\) is -8, then the value of k will be: 1. 32. 23. -24. -3 |
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Answer» Correct Answer - Option 1 : 3 Concept: Sum of elements along principle diagonal = Trace = ∑ Eigen values Product of eigen values = determinant = det (A) Calculation: Given: \(A =\left[ {\begin{array}{*{20}{c}} {1}&{2}&{-1}\\ {3}&{5}&{2}\\ {1}&{k}&{2} \end{array}} \right]\) We know that; Det (A) = product of eigen values 1 × (10 - 2 × k) - 2 × (6 -2) - (3 × k - 5) = -8 10 - 2k - 8 - 3k + 5 = -8 7 - 5k = -8 15 = 5k k = 3 |
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