What is the solution of the Matrix Equation?? HELP

- anonymous

What is the solution of the Matrix Equation?? HELP

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- anonymous

|dw:1370438194862:dw|

- anonymous

@terenzreignz anyone? help!!

- terenzreignz

This is a system...

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## More answers

- terenzreignz

5x - 2y = 2
2x - y = -4

- anonymous

Ok, how do I start to solve it to find my answer?

- terenzreignz

Well, you can start (i recommend)
with the second equation
2x - y = -4
With it, you can add y to both sides
giving you
2x = y - 4
and add 4 to both sides, giving you
2x + 4 = y

- anonymous

Okay, so then I would minus the 2x from each side?

- terenzreignz

No, you have
y = 2x + 4
so replace the "y" in the first equation with (2x+4) and then solve for x.

- anonymous

Okay, I got x=-6.

- terenzreignz

I think you need to redo it... be careful with signs...

- anonymous

This is what I did:
5x-2(2x+4)=2
5x-4x+8=2
1x+8=2
plus -8 on both sides
1x=-6
divided by 1 on both sides
x=-6

- terenzreignz

ohh it should be -8
- distributes to the +8 as well

- amistre64

are we spose to be practicing our matrix maths? or simply finding a solution?

- terenzreignz

amistre to the rescue.....
LOL
@icedancerfigureskater
I'm not good at teaching matrices... but it looks like you're in good hands now :3

- amistre64

the solution setup is correct:
5x - 2y = 2
2x - y = -4
this can be put into a coeff matrix
5 -2 2
2 -1 -4
and augmented thru elementary row operations to get:
1 0 x
0 1 y

- amistre64

the elementary row operation relate to the "elimination" processes of systems of equations

- amistre64

5 -2 2 ; times 2
2 -1 -4 ; times -5
10 -4 4
-10 5 20 add em up for a new Row 2
5 -2 2
0 1 24 ; times by 2
5 -2 2
0 2 48 add em up for a new row 1
5 0 50 ; divide by 5 to 1 up the front
0 1 24
1 0 10
0 1 24 the last column is the solution

- anonymous

@amistre64 I'm learning about Vectors right now. So I have to find a solution to this problem. Would it help if I showed you my answers? And LOL thanks @terenzreignz

- amistre64

you might not have come across an inverse of a matrix yet, but its simple enough; swap some elements, negate others, divide by determinant
5 -2
2 -1 swap 5 and -1
-1 -2
2 5 negate the other 2
-1 2
-2 5 divide all elements by det ...
what is the determinnat?
-(-4)
5 -2
2 -1 det = -5+4 = -1
+(-5)
this gives the inverse as:
1 -2
2 -5
the reason for an inverse is so that we can do some algebra
Ax = b --> x = inv(A)b

- amistre64

|dw:1370440537331:dw|

- anonymous

Oh wow. Haha thanks. Would you mind helping me with a few more? @amistre64

- amistre64

cant, i just took a little break from my paying job to refresh some brain cells .. have to get back to work :)

- anonymous

Ok, haha. Do you know anyone online who could help?

- amistre64

terenz is fine, and could prolly use the matrix math practice ;)

- anonymous

Haha ok thanks! @amistre64

- amistre64

good luck

- terenzreignz

hah... I'm fine apparently :D

- anonymous

lol :D @terenzreignz could you help me with this problem then?
write the system as a matrix equation. Then identify the coefficient matrix, the variable matrix, and the constant matrix.
{ 6a + 5b - 5c = 6
{-7a + 7b +4c = 6
{-7a - 4b - 9c = -1

- terenzreignz

oh sure :)
We have two column matrices...
\[\Large \left[\begin{matrix}a\\b\\c\end{matrix}\right]\]
and
\[\Large \left[\begin{matrix}6\\6\\-1\end{matrix}\right]\]

- terenzreignz

any ideas where I got these?

- anonymous

for each equation there is an a b c variable for each number, and I would imagine you got the 6,6,-1 from the number after the equals sign for each equation.

- terenzreignz

yes :D
the abc one is the variable matrix
while the 66 -1 one is the constant matrix...
So I take it you can guess what the "coefficient" matrix is? :)

- anonymous

would the coefficient matrix be the 6,6,-1?

- anonymous

oh nevermind

- terenzreignz

No, I just told you that the 66-1 is the constant matrix :D

- anonymous

but wait, my answers aren't how they are on here though. it says that my coefficient answer is the 6,6,-1, and the constant matrix is the a,b,c. i'm confused now. do you want me to post my options for answers?

- terenzreignz

sure

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