SOLUTION: How do I solve the following system of equation using matrices? x-3y+z= -21 2x-y+z=-9 2x+y+5z=-31 Thanks in advance!

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Question 471062: How do I solve the following system of equation using matrices?
x-3y+z= -21
2x-y+z=-9
2x+y+5z=-31
Thanks in advance!
Answer by ccs2011(207) About Me  (Show Source):
You can put this solution on YOUR website!
Let A be the coefficient matrix:
A=matrix%283%2C3%2C1%2C-3%2C1%2C2%2C-1%2C1%2C2%2C1%2C5%29
Let B be the constant matrix:
B=matrix%283%2C1%2C-21%2C-9%2C-31%29
Let X be the variable matrix:
X=matrix%283%2C1%2Cx%2Cy%2Cz%29
Then A%2AX+=+B
Using matrix identity property: A%5E-1+%2AA+=+I
where A%5E-1 is the inverse of matrix A and I is the identity matrix.
Multiply both sides by the inverse matrix A%5E-1
X+=+A%5E-1+%2AB
Using a graphing calculator to multiply matrices:
X=matrix%283%2C1%2C2%2C5%2C-8%29
Therefore,
x = 2
y = 5
z = -8