Question

The determinant of the matrix whose eigen values are 7, 1, 9 is given by ________

(a) 7

(b) 63

(c) 9

(d) 17

The question was asked at a job interview.

This intriguing question comes from Transformation (Reduction) of Quadratic Form to Canonical Form topic in chapter Eigen Values and Eigen Vectors of Engineering Mathematics

Answer 1

Right choice is (b) 63

The explanation is: The product of the eigen values of a matrix gives the determinant of the matrix,

Therefore, ∆ = 63.