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

Question

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

amistre64 · Answer

an augment might be beneficial

amistre64 · Answer

unless you know how to work an inverse?

Ax = b

A'Ax = A'b

Ix = A'b

x = A'b

anonymous · Answer

how can i plug in matrices?

amistre64 · Answer

what are you working with?

ti83?

anonymous · Answer

No. I meant how can I plug in matrices on Openstudy

anonymous · Answer

So I can show the equation correctly

amistre64 · Answer

its labor intensive, but i did make an app for it, if you are using a laptop or desktop that is

amistre64 · Answer

http://assets.openstudy.com/updates/attachments/4dfe63b10b8bbe4f12e73631-amistre64-1308517305050-matrix.html

amistre64 · Answer

$$\left[ \begin{array}c 12 &  7\5 &  3\\end{array} \right]
x=
\left[ \begin{array}c 2 &  -1\3 &  2\\end{array} \right]$$

anonymous · Answer

$$\[\left[ \begin{array}c 12 &  7\5 &  3\\end{array} \right]$$ X = $$\left[ \begin{array}c 2 &  -1\3 &  2\\end{array} \right]$$\]

anonymous · Answer

hows that?

anonymous · Answer

yeah

amistre64 · Answer

it was designed to post one matrix hence the oddity of trying multiples, but knowing the latex sorts it out

amistre64 · Answer

so, how do we approach this?  inverse are augment?  either way is fine.

inverse may be simpler in this case tho

amistre64 · Answer

we can augment it as this, and row reduce.
$$\left[ \begin{array}c 12 & 7 & | & 2 &  -1\5 & 3 & | & 3 &  2\\end{array} \right]$$

anonymous · Answer

how do you reduce it

amistre64 · Answer

elementary row operations for course,

get the left side worked into the identity matrix.  and the right side works itself into x

amistre64 · Answer

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

amistre64 · Answer

http://www.wolframalpha.com/input/?i=rref%7B%7B12%2C7%2C2%2C-1%7D%2C%7B5%2C3%2C3%2C2%7D%7D

amistre64 · Answer

did you try for an inverse?

amistre64 · Answer

-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