Question 899754: Solve the system of linear equations using the Gauss-Jordan elimination method.
2x + 2y + z = −7
x + z = −3
4y − 3z = 13
Answer by richwmiller(17219)   (Show Source):
You can put this solution on YOUR website! 2,2,1,-7
1,0,1,-3
0,4,-3,13
divide row 1 by 2
1,1,1/2,-7/2
1,0,1,-3
0,4,-3,13
add down (-1) *row 1 to row 2
1,1,1/2,-7/2
0,-1,1/2,1/2
0,4,-3,13
add down (0) *row 1 to row 3
1,1,1/2,-7/2
0,-1,1/2,1/2
0,4,-3,13
divide row 2 by -1
1,1,1/2,-7/2
0,1,1/-2,1/-2
0,4,-3,13
add down (-4) *row 2 to row 3
1,1,1/2,-7/2
0,1,1/-2,1/-2
0,0,-1,15
divide row 3 by -1
1,1,1/2,-7/2
0,1,1/-2,1/-2
0,0,1,-15
We now have the value for the last variable.
We will work our way up and get the other solutions.
add up (1/2) *row 3 to row 2
1,1,1/2,-7/2
0,1,0,-8
0,0,1,-15
add up (-1/2) *row 3 to row 1
1,1,0,4
0,1,0,-8
0,0,1,-15
add up (-1) *row 2 to row 1
1,0,0,12
0,1,0,-8
0,0,1,-15
"12","-8","-15"
(12,-8,-15)
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