Fp1 matrix algebra inverses Watch

ben789
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Hey, I am a bit confused here. Hoping someone with a knowledge of matrices can help me out.

As matrix algebra is not commutative, how do I know which side to put the A^-1 on of the matrices to ensure I get the right answer when solving these sort of problems? (shown in the picture)

I hope I have conveyed myself clearly
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Notnek
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(Original post by ben789)
Hey, I am a bit confused here. Hoping someone with a knowledge of matrices can help me out.

As matrix algebra is not commutative, how do I know which side to put the A^-1 on of the matrices to ensure I get the right answer when solving these sort of problems? (shown in the picture)

I hope I have conveyed myself clearly
With matrix equations, you can either multiply the equation by a matrix either 'on the left' or 'on the right'.


E.g. AC = B


If you multiply both sides of the equation by A^{-1} on the left, you get

A^{-1} A C = A^{-1} B

and the A^{-1} and A cancel to give

 C = A^{-1} B


If instead you were to multiply the original equation by A^{-1} on the right, then you would get

ACA^{-1} = BA^{-1}

but this is not useful here since no matrices cancel.


So for matrix equations, you always need to choose the best direction to multiply your equation by. Does that help?
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ben789
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(Original post by notnek)
With matrix equations, you can either multiply the equation by a matrix either 'on the left' or 'on the right'.


E.g. AC = B


If you multiply both sides of the equation by A^{-1} on the left, you get

A^{-1} A C = A^{-1} B

and the A^{-1} and A cancel to give

 C = A^{-1} B


If instead you were to multiply the original equation by A^{-1} on the right, then you would get

ACA^{-1} = BA^{-1}

but this is not useful here since no matrices cancel.


So for matrix equations, you always need to choose the best direction to multiply your equation by. Does that help?
Yes that has cleared it up 100%, thanks for your answer, its very much appreciated.
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