Question

Find the eigen value and corresponding eigen vectors of the matrix A=[[8,-6,2],[-6,7,-4],[2,-4,3]]

Answer 1

To find the eigenvalues and eigenvectors of a matrix, solve the characteristic equation and substitute the eigenvalues back into the original equation.

Step-by-step explanation:

To find the eigenvalues and corresponding eigenvectors of a matrix, we need to first find the eigenvalues by solving the characteristic equation. The characteristic equation is obtained by subtracting a scalar multiple of the identity matrix from the given matrix A and setting the determinant equal to zero.

Using the formula |A - λI| = 0, we can calculate the eigenvalues of matrix A. Once we have the eigenvalues, we can find the eigenvectors by substituting them back into the original equation (A - λI)v = 0, where v is the eigenvector.

By following these steps, we can find the eigenvalues and corresponding eigenvectors of matrix A.