Inverses: B is inverse of A; find X so XA = C for C =....  TOPIC_SOLVED

Linear spaces and subspaces, linear transformations, bases, etc.

Inverses: B is inverse of A; find X so XA = C for C =....

Postby mental on Tue Mar 10, 2009 5:09 pm

Does anyone know how to solve for:
Matrix A has inverese

B= [ 2 1 3 ]
1 1 1
4 2 1

I need to find a matrix X such that XA=C, where

C= [ 1 2 3 ]
1 0 1
0 0 0

Any ideas will be helpful. Thanks
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Postby stapel_eliz on Tue Mar 10, 2009 6:33 pm

mental wrote:Matrix A has inverese

B= [ 2 1 3 ]
1 1 1
4 2 1

I need to find a matrix X such that XA=C, where

C= [ 1 2 3 ]
1 0 1
0 0 0

You are given that AB = BA = I, the identity matrix. You are given B and C. You are asked to solve "XA = C" for X.

To solve using inverses, multiply each side of the equation, "on the right", by the inverse of A:

. . . . .(XA)A-1 = (C)A-1

This leaves you with X(AA-1) = X(I) = X = CA-1 = CB.

Multiply it out to find X. :wink:
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Re: Inverses: B is inverse of A; find X so XA = C for C =....  TOPIC_SOLVED

Postby mental on Wed Mar 11, 2009 12:49 am

Thanks a lot! I actually managed to solve for Y but couldn't rationalize enough to get X. It's greatly appreciated!!!
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