SOLUTION: 5x-3y+7=11 3x+y-2z=11 -x+2y+z=11 Using the matrix method,which row of operations can i use to solve this problem?

Algebra ->  Matrices-and-determiminant -> SOLUTION: 5x-3y+7=11 3x+y-2z=11 -x+2y+z=11 Using the matrix method,which row of operations can i use to solve this problem?      Log On


   

Question 324886: 5x-3y+7=11
3x+y-2z=11
-x+2y+z=11
Using the matrix method,which row of operations can i use to solve this problem?
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
You could find the inverse of the coefficient matrix or you could use Gaussian elimination.
I'll use matrix inversion in EXCEL (MINVERSE function).
[A]=%28matrix%283%2C3%2C5%2C-3%2C7%2C3%2C1%2C-2%2C-1%2C2%2C1%29%29
[x]=%28matrix%283%2C1%2Cx%2Cy%2Cz%29%29
[b]=%28matrix%283%2C1%2C11%2C11%2C11%29%29
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.
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Find the inverse of [A].
[A][x]=[b]
[x]=[A]inv[b]
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.
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det([A])=77
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[A]inv=%281%2F77%29%2A%28matrix%283%2C3%2C5%2C17%2C-1%2C-1%2C12%2C31%2C7%2C-7%2C14%29%29
%28matrix%283%2C1%2Cx%2Cy%2Cz%29%29=%28matrix%283%2C1%2C3%2C6%2C2%29%29