SOLUTION: Matrices Hello I'm needing some help with my homework that asks me to use the matrices to solve each system of equations. If a system has no solution, so indicate. {x-y+z=2

Question 182077: Matrices
Hello I'm needing some help with my homework that asks me to use the matrices to solve each system of equations. If a system has no solution, so indicate.
{x-y+z=2
x+2y-z=6
2x-y-z=3
thanks
Haley
Answer by Alan3354(69443) (Show Source): You can put this solution on YOUR website!
|x - y + z 2|
|x +2y - z 6| = 0
|2x -y - z 3|
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You can leave out the x, y and z.
|1 -1 +1 2|
|1 +2 -1 6| = 0
|2 -1 -1 3|
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First, find the determinant.
DET = 1*(-2-1) + 1*(-1+2) + 1*(-1-4) = -3+1-5
DET = -7
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x*DET = -1(-3+6) -1(6+6) +2(-2-1) =-3-12-6 = -21
x = 3
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-y*DET = 1(-3+6) -1(3-12) +2(-1+2) = 3+9+2 = 14
y = 2
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At this point, I'd substitute to find z, but it says use a matrix.
z*DET = 1(6+6) +1(3-12) +2(-1-4) = 12-9-10 = -7
z = 1
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You can find solvers online to do these, or you can do them with an Excel sheet.
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