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## Homework Statement

Let A be the matrix:

**-5 -3**

18 10

18 10

Find an invertible matrix X so that XAX

^{-1}is diagonal. Use this to find a square root of the matrix A.

## Homework Equations

DetA - xI

(A-[itex]\lambda[/itex]I)v = 0

## The Attempt at a Solution

So, I found DetA- xI, which gave me the eigenvalues 4 and 1. I found the eigenvectors for each value, giving me X =

**-1 -1**

3 2

3 2

Now what confuses me is finding the square root of A. I understand that XD

^{1/2}X

^{-1}will give me that, so would I just multiply X by D

^{1/2}, and then by X

^{-1}? I tried that, and it gave me A=

**-1 -1**

6 4

6 4