1.

If 3, 5 are the eigenvalues of a square matrix A of order 2, then the eigenvalues of the matix A3 will be1. 27, 1252. 9, 153. 3, 54. 9, 25

Answer» Correct Answer - Option 1 : 27, 125

Concept:

If λ is an eigenvalue of a matrix A and k  is a scalar then:

1) λm is the eigenvalue of matrix Am (m belongs to N).

2) kλ  is an eigenvalue of matrix kA.

3) λ + k is an eigenvalue of the matrix A + kI.

4) λ - k  is an eigenvalue of matrix A - kI.

Calculation:

Given:

3, 5 are the eigenvalues then,

Using Property 1;

A3 = λ3 = 33 = 27.

A3 = λ3 = 53 = 125.



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