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## Homework Statement

I have 4 equations.

3x+6y-5z-t=-8

6x-2y+3z+2t=13

4x-3y-z-3t=-1

5x+6y-3z+4t=-6

I have already solved this matrix using gauss elimination and found that x=1, y=2, z=5, t=-2

Now the next part of the question asks to solve the matrix using eigenvalues and eigenvectors.

## Homework Equations

Eigenvalues and Eigenvectors

## The Attempt at a Solution

I have worked through to find the eigenvalues and received this equation

0=L^4 - 4(L^3) - 30(L^2) - 162L + 537, where L is lander

from this I found the Eigen values

2.2522

8.7456

-3.4989-3.8757i

-3.4989+3.8757i

Which I am fairly confident are correct.

However I am unsure about how to continue from here and how the corresponding eigenvectors will solve the matrix.

Thanks Very Much