SOLUTION: solve using matrices 3x-y_z=-15 x+2y-z=1 2x+3y-2z=0

Question 918064: solve using matrices
3x-y_z=-15
x+2y-z=1
2x+3y-2z=0
Answer by richwmiller(17219) (Show Source): You can put this solution on YOUR website!
3,-1,-1,-15
1,2,-1,1
2,3,-2,0
divide row 1 by 3
1,-1/3,-1/3,-5
1,2,-1,1
2,3,-2,0
add down (-1) *row 1 to row 2
1,-1/3,-1/3,-5
0,7/3,-2/3,6
2,3,-2,0
add down (-2) *row 1 to row 3
1,-1/3,-1/3,-5
0,7/3,-2/3,6
0,11/3,-4/3,10
divide row 2 by 7/3
1,-1/3,-1/3,-5
0,1,-6/21,18/7
0,11/3,-4/3,10
add down (-11/3) *row 2 to row 3
1,-1/3,-1/3,-5
0,1,-2/7,18/7
0,0,-18/63,12/21
divide row 3 by -2/7
1,-1/3,-1/3,-5
0,1,-2/7,18/7
0,0,1,-2
We now have the value for the last variable.
We will work our way up and get the other solutions.
add up (2/7) *row 3 to row 2
1,-1/3,-1/3,-5
0,1,0,2
0,0,1,-2
add up (1/3) *row 3 to row 1
1,-3/9,0,-17/3
0,1,0,2
0,0,1,-2
add up (1/3) *row 2 to row 1
1,0,0,-5
0,1,0,2
0,0,1,-2
final
1,0,0,-5
0,1,0,2
0,0,1,-2
1,0,0,-5
0,1,0,2
0,0,1,-2
"-5","2","-2"
(-5,2,-2)

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