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

Linear spaces and subspaces, linear transformations, bases, etc.
mental
Posts: 2
Joined: Tue Mar 10, 2009 5:05 pm
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### Inverses: B is inverse of A; find X so XA = C for C =....

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

stapel_eliz
Posts: 1628
Joined: Mon Dec 08, 2008 4:22 pm
Contact:
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.

mental
Posts: 2
Joined: Tue Mar 10, 2009 5:05 pm
Contact:

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

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