A 3 × 3 matrix has eigenvalues 1, 2 and 5. The determinant of the matrix is              .

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