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If the product of two eigen values of the matrix \(\begin{bmatrix} 6 & -2 & 2 \\\ -2 & 3 & -1 \\\ 2 & -1 & 3 \end{bmatrix}\) is 16, then third eigen value is1. 22. -23. 364. 6 |
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Answer» Correct Answer - Option 1 : 2 Explanation: \(\left[ A \right] = \left[ {\begin{array}{*{20}{c}} 6&{ - 2}&2\\ { - 2}&3&{ - 1}\\ 2&{ - 1}&3 \end{array}} \right]\) As we know: Product of Eigen values = Determinant of matrix Determinant of matrix = 6 × (9 – 1) – (- 2) (- 6 + 2) + 2 (2 - 6) Determinant of matrix = 48 – 8 – 8 ∴ Determinant of matrix = 32 Now, Let the third Eigen value be x Product of Eigen value = Determinant of [A] 16 × x = 32 ∴ x = 2 ∴ Third Eigen value = 2 |
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