Q. A 3 × 3 matrix has eigenvalues 1, 2 and 5. The determinant of the matrix is .
Sol:
Given that, Eigen values of a matrix
λ1 = 1, λ2 = 2, λ3 = 5
From the property of Eigen values,
Determinant of a matrix = product of its Eigen values
⇒ Determinant = λ1 λ2 λ3 = (1) (2) (5) = 10
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