SOLUTION: use the matrix method to solve the system of linear equations: x+ y- z= 0 3x- y+3z=-2 x+2y-3z=-1

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Question 662746: use the matrix method to solve the system of linear equations:
x+ y- z= 0
3x- y+3z=-2
x+2y-3z=-1

Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
1     1    -1     0
3    -1     3    -2
1     2    -3    -1


1     1    -1     0
0    -4     6    -2    R2 - 3R1
1     2    -3    -1



1     1    -1     0
0    -4     6    -2
0     1    -2    -1   R3 - R1


1    1   -1     0
0    1   -1.5   0.5  (1/4)*R2
0    1   -2     1


1    1   -1      0
0    1   -1.5    0.5
0    0   -0.5   -1.5   R3 - R2


1    1   -1      0
0    1   -1.5    0.5
0    0    1      3    -2*R3


1    1   -1      0
0    1   -1.5    0.5
0    0    1      3    -2*R3


1     1    -1     0
0     1     0     5   R2 + 1.5*R3
0     0     1     3


1     1     0     3   R1 + R3
0     1     0     5
0     0     1     3


1     0     0    -2   R1 - R2
0     1     0     5
0     0     1     3

So x = -2, y = 5 and z = 3