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## Homework Statement

The problem is setting up the equation, it says that the matrix equation will be made up of four equations for the 2 unknowns.

I'm supposed to find for which a's and b's the equation is true, using a linear system and gaussian elimination.

## Homework Equations

A

^{2}+ aA + bI

_{2}= 0

A = | 3 1|

......| 4 -2|

I

_{2}= identity matrix, 2x2

A

^{2}= | 13 5 |

.......| 4 8 |

## The Attempt at a Solution

I'm not sure how to proceed with this problem.

How do I split the equation into 4 equations with respect to the variables a and b?

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