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Finding the square root of a matrix!

  • Thread starter smerhej
  • Start date
  • #1
20
0

Homework Statement



Let A be the matrix:
-5 -3
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

Now what confuses me is finding the square root of A. I understand that XD1/2X-1 will give me that, so would I just multiply X by D1/2 , and then by X-1? I tried that, and it gave me A=

-1 -1
6 4
 

Answers and Replies

  • #2
I like Serena
Homework Helper
6,577
176
If you multiply your final matrix by itself, what do you get?
 
  • #3
20
0
The original matrix A! Thank you! I don't know how I didn't think of that to check my work..
 
  • #4
I like Serena
Homework Helper
6,577
176
:smile:
 

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