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 Post subject: How to square a square matrix?Posted: Fri, 1 Oct 2010 20:45:44 UTC
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Joined: Fri, 1 Oct 2010 20:31:32 UTC
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the matrix A is a 3x3 that looks like...
5 -3 2
15 -9 6
10 -6 4

I am supposed to find A^2 ..when i square A I get zeros in all of the spots. Am i supposed to be getting this answer? When you square a square matrix is it always zeros or is this just a special problem?

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 Post subject: Re: How to square a square matrix?Posted: Fri, 1 Oct 2010 21:52:39 UTC
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Joined: Wed, 30 Mar 2005 04:25:14 UTC
Posts: 12097
Location: Austin, TX
lauren72 wrote:
the matrix A is a 3x3 that looks like...
5 -3 2
15 -9 6
10 -6 4

I am supposed to find A^2 ..when i square A I get zeros in all of the spots. Am i supposed to be getting this answer? When you square a square matrix is it always zeros or is this just a special problem?

You should try squaring ANY OTHER MATRIX, and you'll most likely get a different answer from 0. Heck, try squaring the IDENTITY MATRIX. If ever you have a question like this, you should try some other examples to see if it's true then. That's the easiest way to figure out most of these kinds of questions.

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 Post subject: Re: How to square a square matrix?Posted: Sun, 3 Oct 2010 12:44:01 UTC
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Joined: Mon, 19 May 2003 19:55:19 UTC
Posts: 7949
Location: Lexington, MA
Hello, lauren72!

Quote:
Given: .

I am supposed to find
When i square , I get zeros in all of the spots. . It happens . . .

Am i supposed to be getting this answer? . yes
When you square a square matrix is it always zeros . no!
or is this just a special problem? . yes

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 Post subject: Re: How to square a square matrix?Posted: Mon, 4 Oct 2010 23:23:30 UTC
 Member of the 'S.O.S. Math' Hall of Fame

Joined: Wed, 21 May 2003 04:27:18 UTC
Posts: 990
lauren72 wrote:
the matrix A is a 3x3 that looks like...
5 -3 2
15 -9 6
10 -6 4

I am supposed to find A^2 ..when i square A I get zeros in all of the spots. Am i supposed to be getting this answer? When you square a square matrix is it always zeros or is this just a special problem?

Two reasons this happened:

(1) When you row reduce your given matrix, you get two rows of zeros in the row reduced echleon form...

and

(2) Attempt to diagonalize it (if you know how to do it). You will get an interesting eigenvalue!

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G.H. Hardy (1877-1947)

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