anonymous
  • anonymous
What is the solution of the Matrix Equation?? HELP
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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jamiebookeater
  • jamiebookeater
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anonymous
  • anonymous
|dw:1370438194862:dw|
anonymous
  • anonymous
@terenzreignz anyone? help!!
terenzreignz
  • terenzreignz
This is a system...

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terenzreignz
  • terenzreignz
5x - 2y = 2 2x - y = -4
anonymous
  • anonymous
Ok, how do I start to solve it to find my answer?
terenzreignz
  • 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
  • anonymous
Okay, so then I would minus the 2x from each side?
terenzreignz
  • terenzreignz
No, you have y = 2x + 4 so replace the "y" in the first equation with (2x+4) and then solve for x.
anonymous
  • anonymous
Okay, I got x=-6.
terenzreignz
  • terenzreignz
I think you need to redo it... be careful with signs...
anonymous
  • 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
  • terenzreignz
ohh it should be -8 - distributes to the +8 as well
amistre64
  • amistre64
are we spose to be practicing our matrix maths? or simply finding a solution?
terenzreignz
  • 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
  • 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
  • amistre64
the elementary row operation relate to the "elimination" processes of systems of equations
amistre64
  • 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
  • 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
  • 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
  • amistre64
|dw:1370440537331:dw|
anonymous
  • anonymous
Oh wow. Haha thanks. Would you mind helping me with a few more? @amistre64
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
  • anonymous
Ok, haha. Do you know anyone online who could help?
amistre64
  • amistre64
terenz is fine, and could prolly use the matrix math practice ;)
anonymous
  • anonymous
Haha ok thanks! @amistre64
amistre64
  • amistre64
good luck
terenzreignz
  • terenzreignz
hah... I'm fine apparently :D
anonymous
  • 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
  • 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
  • terenzreignz
any ideas where I got these?
anonymous
  • 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
  • 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
  • anonymous
would the coefficient matrix be the 6,6,-1?
anonymous
  • anonymous
oh nevermind
terenzreignz
  • terenzreignz
No, I just told you that the 66-1 is the constant matrix :D
anonymous
  • 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
  • terenzreignz
sure

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