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April 29, 2024, 05:31:24 pm
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Author Topic: Matrix Equation  (Read 1190 times)  Share 

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Matrix Equation
« on: January 21, 2008, 12:37:08 am »
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How do you solve

YA = B

for Y if Y, A, and B are all 2 by 2 matrices?
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Collin Li

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Re: Matrix Equation
« Reply #1 on: January 21, 2008, 01:00:04 am »
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Multiply both sides by the multiplicative inverse of A? To find this, you have to do some row operations with the identity matrix.

I don't remember matrices. Can't you divide (LOL I'm not sure if that's possible)?
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Collin Li

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Re: Matrix Equation
« Reply #2 on: January 21, 2008, 01:08:40 am »
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(in that order, matrices are not commutative in multiplication)

I think LaTeX is stuffed up...
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DrowNz

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Re: Matrix Equation
« Reply #3 on: January 21, 2008, 02:56:50 am »
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you can't divide matrices. you take the multiplicative inverse (it's like multiplying something by 1/3 instead of dividing it by 3) of A from both sides and hence Y = BA^-1
« Last Edit: January 21, 2008, 02:59:47 am by DrowNz »
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Re: Matrix Equation
« Reply #4 on: January 21, 2008, 02:06:10 pm »
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nvm.. i get it now :P Thanks a lot people

« Last Edit: January 21, 2008, 02:12:55 pm by DivideBy0 »
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doboman

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Re: Matrix Equation
« Reply #5 on: January 21, 2008, 02:07:37 pm »
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Shouldnt it be Y=A^-1B
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Collin Li

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Re: Matrix Equation
« Reply #6 on: January 21, 2008, 02:08:47 pm »
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Ah, but you mixed up your notation. should be , I think.
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Re: Matrix Equation
« Reply #7 on: January 21, 2008, 02:52:53 pm »
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btw did you just find this by inspection, or are there actual steps to reach it?
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Collin Li

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Re: Matrix Equation
« Reply #8 on: January 21, 2008, 02:58:33 pm »
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Nah, pretty much just by inspection:


(where is the 2x2 identity matrix - multiplying by the identity matrix is the equivalent of multiplying by 1 in numbers)


If you are actually given , there are a series of steps required to find .
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