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GATE CS 2016 Official Paper: Shift 1

IBPS SO IT Officer Mains: Full Mock Test

4845

60 Questions
60 Marks
45 Mins

**Concept:**

Eigenvalues are the roots of the characteristic equation and determinant of a matrix is the product of its eigenvalues.

**Calculation:**

We have to consider a 3 × 3 matrix, so roots will be 3 means 3 eigenvalues. Two eigenvalues are given as : (2 + √-1) and 3.

As 3 × 3 is a real matrix, in real matrix roots can never be imaginary. We have to take the complex roots in pair. So,

Three eigenvalues are:

2 + i , 2 – i, and 3

Determinant of the matrix P = product of its eigenvalues

= (2 + i) × (2 - i) × 3

= (4 – i^{2}) × 3 = (4 – (–1)) × 3

= 5 × 3 = 15