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October 29th, 2010, 12:44 AM   #1
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Matrix right inverse

Find all right-inverses of the matrix

Attempt:



(A | R):

=

Now I tried to get the matrix into the form of (I | R) by gauss reduction:



but this will never work since the matrix on the left is 2 x 3 and not 2 x 2 and thus I will never get on the left

What can I do?
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October 29th, 2010, 02:17 PM   #2
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Re: Matrix right inverse

Shootin in the dark, here...

Write out what the actual elements of the product would be on the left hand side...

since the matrix on the right hand side has a "1" in it's upper left hand.

Now I'll write the lower left hand element...



Add twice the first equation I wrote to the second...

-->

The process is similar for the y's. You solution will be any matrix of the form that you wrote, where and is free.
(Well, this, plus the similar result for the y's...)
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October 29th, 2010, 03:39 PM   #3
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Re: Matrix right inverse

The answer in my notes was: where , I am confused as I dont see the similarity to:

and
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October 29th, 2010, 08:51 PM   #4
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Re: Matrix right inverse

If you sub those values for x2 and y2 back into the equations, you'll get something more easily comparable to the given solution
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