# 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

Algebra ->  Algebra  -> Equations -> 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       Log On

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 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 HaleyAnswer by Alan3354(30968)   (Show Source): You can put this solution on YOUR website!|x - y + z 2| |x +2y - z 6| = 0 |2x -y - z 3| --------------- You can leave out the x, y and z. |1 -1 +1 2| |1 +2 -1 6| = 0 |2 -1 -1 3| ----------- First, find the determinant. DET = 1*(-2-1) + 1*(-1+2) + 1*(-1-4) = -3+1-5 DET = -7 ----------- x*DET = -1(-3+6) -1(6+6) +2(-2-1) =-3-12-6 = -21 x = 3 ----------- -y*DET = 1(-3+6) -1(3-12) +2(-1+2) = 3+9+2 = 14 y = 2 ------------- 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 ---------- You can find solvers online to do these, or you can do them with an Excel sheet.