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Multiplication/division of matrices and vectors 
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#1
Mar2714, 05:03 AM

P: 686

1) Let A a square matrix, x a colum vector and b another colum vector. So, I want solve for x the following equation: Ax=b
So: x=b÷A = b×A^{1} And this is the answer! Or would be this the correct answer x = A^{1}×b ? 2) Is possible to solve the equation above for A ? How? 


#2
Mar2714, 06:11 AM

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Anyway, you want to solve ##A\mathbf{x} = \mathbf{b}##. First of all, ##A## might not be an invertible matrix, in which case, you can't always solve this system (and if you can, the solution might not be unique!). If your matrix is invertible, then you can multiply the equation on the left with ##A^{1}## and you get [tex]\mathbf{x} = A^{1}A\mathbf{x} = A^{1}\mathbf{b}[/tex] Multiplying the equation on the right doesn't work since you'll get [tex]A\mathbf{x}A^{1} = \mathbf{b}A^{1}[/tex] We can't simplify the lefthand side due to noncommutativity. 


#3
Mar2714, 10:37 AM

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#4
Mar2714, 11:35 AM

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Multiplication/division of matrices and vectors



#5
Mar2714, 12:29 PM

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P: 21,304

If Ax = b, and A is invertible, then multiply on the left by A^{1}. 


#6
Mar2714, 12:30 PM

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#7
Mar2714, 12:33 PM

P: 686

Edit: thanks for everyone from topic!!! Edit2: So, Independent of the uniqueness, you are saying that is not possible to isolate A in Ax=b ? 


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