## anonymous one year ago matrix equation help? {{12,7},{5,3}}x={{2,-1},{3,2}}

1. amistre64

an augment might be beneficial

2. amistre64

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

3. anonymous

how can i plug in matrices?

4. amistre64

what are you working with? ti83?

5. anonymous

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

6. anonymous

So I can show the equation correctly

7. amistre64

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

8. amistre64
9. amistre64

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

10. anonymous

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

11. anonymous

hows that?

12. anonymous

yeah

13. amistre64

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

14. amistre64

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

15. amistre64

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

16. anonymous

how do you reduce it

17. amistre64

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

18. amistre64

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

19. amistre64
20. amistre64

did you try for an inverse?

21. amistre64

-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