Question

Let us consider a square matrix A of order n with Eigen values of a, b, c then the Eigen values of the Transpose of A could be

Answer 1

Given : a square matrix A of order n with Eigen values of a, b, c

To Find : Eigen values of the Transpose of A

Solution:

Eigen value of a matrix and its transpose are same.

Eigen value of given square matrix are a , b & c

Hence Eigen value of transpose of given matrix would also be  

a , b , c

Eigen values of the Transpose of A could be  a, b and c

Eigen values of a matrix are roots of its characteristic polynomial.

matrices A and $A^T$ have the same characteristic polynomial

Hence Eigen values of a matrix and its transpose are same

Learn More:

Find the inverse of the following matrix by using row elementary ...

brainly.in/question/18338344

If A= matrix [ 2 1 1 1 0 1 0 2 -1],find the inverse of A using elementary ...

brainly.in/question/17274361

Answer 2

Given :-

A square matrix A of order n with Eigen values of a, b, c

To Find :-

Eigen values of the Transpose of A

Solution:-

Eigen value of a matrix and its transpose are same.

Eigen value of given square matrix are a , b & c

Hence Eigen value of transpose of given matrix would also be a , b , c

Eigen values of the Transpose of A could be a, b and c

Eigen values of a matrix are roots of its characteristic polynomial.

Matrices A and A^T have the same characteristic polynomial

Hence Eigen values of a matrix and its transpose are same$.$