How can I find the matrix in this equation?

Me and my friend are having much difficulty on this question and any help on solving it would be greatly appreciated. We're both new to this whole linear algebra thing and we can say in confidence that our professor has extremely poor communication skills.

Here is what we got:

http://i.imgur.com/b6gqg.jpg

Any insight on how to solve this for two freshman would be much appreciated :D thanks!

Re: How can I find the matrix in this equation?

what you have is an equation of the form:

$\displaystyle AB + C^{-1} = D$ solve this like an ordinary algebra problem: first add $\displaystyle -C^{-1}$ to both sides:

$\displaystyle AB = D-C^{-1}$. then multiply both sides by $\displaystyle B^{-1}$ (hopefully B is invertible, or this will be a problem):

$\displaystyle A = (D-C^{-1})B^{-1}$ it's important to multiply matrices in the proper order, AB is usually NOT the same as BA.

Re: How can I find the matrix in this equation?

YES! We got it! What's strange is we did that same process to other problems but got them incorrect :/ We managed to get this one correct though, thank you very much Deveno!

Before you leave though, do you mind helping us with one more problem? We tried solving this one but alas came up with the wrong answer.

http://i.imgur.com/Cnnox.jpg

Thank you so much for your help for our previous problem, if you could help us with one more, that'd be so appreciated! In return, we shall lurk the forum and help out any more basic math problems we stumble upon :)

Thanks again :D

Re: How can I find the matrix in this equation?

here your equation is of the form:

$\displaystyle AB + 4C^{-1} = D$ so we start by subtracting $\displaystyle 4C^{-1}$ from both sides:

$\displaystyle AB = D - 4C^{-1}$, then multiplying (on the right) by $\displaystyle B^{-1}$ :

$\displaystyle A = (D - 4C^{-1})B^{-1}$.

so, calculate $\displaystyle C^{-1}$ first, multiply that by -4 (every entry), and add to D. multiply the result (on the right) by $\displaystyle B^{-1}$.

Re: How can I find the matrix in this equation?

Ah yes! Thank you! We figured out that what we did wrong was we assumed a different order of operations - we were trying to copy an example from a textbook.

We got it, thanks a lot friend! Glad you're here to save the day =D