matrix equation help? {{12,7},{5,3}}x={{2,-1},{3,2}}

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matrix equation help? {{12,7},{5,3}}x={{2,-1},{3,2}}

Mathematics
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an augment might be beneficial
unless you know how to work an inverse? Ax = b A'Ax = A'b Ix = A'b x = A'b
how can i plug in matrices?

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what are you working with? ti83?
No. I meant how can I plug in matrices on Openstudy
So I can show the equation correctly
its labor intensive, but i did make an app for it, if you are using a laptop or desktop that is
http://assets.openstudy.com/updates/attachments/4dfe63b10b8bbe4f12e73631-amistre64-1308517305050-matrix.html
\[\left[ \begin{array}c 12 & 7\\5 & 3\\\end{array} \right] x= \left[ \begin{array}c 2 & -1\\3 & 2\\\end{array} \right]\]
\[\[\left[ \begin{array}c 12 & 7\\5 & 3\\\end{array} \right]\] X = \[\left[ \begin{array}c 2 & -1\\3 & 2\\\end{array} \right]\]\]
hows that?
yeah
it was designed to post one matrix hence the oddity of trying multiples, but knowing the latex sorts it out
so, how do we approach this? inverse are augment? either way is fine. inverse may be simpler in this case tho
we can augment it as this, and row reduce. \[\left[ \begin{array}c 12 & 7 & | & 2 & -1\\5 & 3 & | & 3 & 2\\\end{array} \right]\]
how do you reduce it
elementary row operations for course, get the left side worked into the identity matrix. and the right side works itself into x
divide row1 by 12 and multiply by -5 and add to row2 12,7,2,-1 1,7/12,2/12,-1/12 -5,-35/12,-10/12,5/12 5, 3, 3, 2 -5,-35/12,-10/12, 5/12 5, 36/12, 36/12,24/12 ---------------------- 0, 1/12, 26/12, 29/12 multiply by 12 0, 1, 26, 29 new setup 1, 7/12, 2/12, -1/12 0, 1 , 26 , 29 multiply row 2 by -7/12 and add it to row1 1, 7/12, 2/12, -1/12 0, -7/12 , -26(7)/12 , -29(7)/12 -------------------------------- 1, 0 , -90/6 , -204/12 1, 0 , -15 , -17 1, 0, -15, -17 0, 1, 26, 29 I x
http://www.wolframalpha.com/input/?i=rref%7B%7B12%2C7%2C2%2C-1%7D%2C%7B5%2C3%2C3%2C2%7D%7D
did you try for an inverse?
-35 12 7 5 3 36 det = 1 by some basic shortcut, A' has a pattern swap corners and negate the other 2 A' = 3 -7 -5 12

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