SOLUTION: Could you please help me solve this system of equations by using A^-1? x+5y+5z=-7 x+4y+5z=-5 x+5y+4z=-5

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Question 151583: Could you please help me solve this system of equations by using A^-1?
x+5y+5z=-7
x+4y+5z=-5
x+5y+4z=-5

Answer by Edwin McCravy(20060) About Me  (Show Source):
You can put this solution on YOUR website!
Could you please help me solve this system of equations by using A%5E-1?
x+5y+5z=-7
x+4y+5z=-5
x+5y+4z=-5

We form the matrix equation A%2AX=B where

A=%28matrix%283%2C3%2C1%2C5%2C5%2C1%2C4%2C5%2C1%2C5%2C4%29%29, B=%28matrix%283%2C1%2C-7%2C-5%2C-5%29%29,  X=%28matrix%283%2C1%2Cx%2Cy%2Cz%29%29 

So the matrix equation is A%2AX=B or

  A  * X =  B     
 

Do you know how to find the inverse of a matrix?
If not post again asking how.  The inverse of 
matrix A is:

A%5E%28-1%29=%28matrix%283%2C3%2C-9%2C5%2C5%2C1%2C-1%2C0%2C1%2C0%2C-1%29%29

So we left-multiply both sides of the equation by this
inverse matrix, A%5E%28-1%29



Do you know how to multiply matrices?  If not
post again asking how.

Multiply the matrices and get this:



%28matrix%283%2C1%2Cx%2Cy%2Cz%29%29=%28matrix%283%2C1%2C13%2C-2%2C-2%29%29

So x=13, y=-2, z=-2

Edwin