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Question 828004: 2x-y+2z=-8,x+2y-3z-9=0,3x-y-4z=3
Answer by jsmallt9(3758)   (Show Source):
You can put this solution on YOUR website! Please include the instructions for your problems. I'm guessing that we are supposed to solve this system of equations. And since you posted it in the "Matrices, ..." category I'm guessing that you/we are supposed to use matrices or determinants to solve the system.
Algebra.com does not draw matrices well. So I am just going to show you the rectangular array of numbers (without the usual brackets).
2x - y + 2z = -8
x + 2y - 3z - 9 = 0
3x - y - 4z = 3
The middle equation is not quite in the proper form. Adding 9 to both sides of it we get:
2x - y + 2z = -8
x + 2y - 3z = 9
3x - y - 4z = 3
Initial augmented matrix:
2 -1 2 -8
1 2 -3 9
3 -1 -4 3
Replace row 1 with 1/2 times row 1.
1 -1/2 1 -4
1 2 -3 9
3 -1 -4 3
Add -1 times row 1 to row 2.
1 -1/2 1 -4
0 5/2 -4 13
3 -1 -4 3
Add -3 times row 1 to row 3.
1 -1/2 1 -4
0 5/2 -4 13
0 1/2 -7 15
Replace row 2 with 2/5 times row 2.
1 -1/2 1 -4
0 1 -8/5 26/5
0 1/2 -7 15
Add 1/2 times row 2 to row 1.
1 0 1/5 -7/5
0 1 -8/5 26/5
0 1/2 -7 15
Add -1/2 times row 2 to row 3.
1 0 1/5 -7/5
0 1 -8/5 26/5
0 0 -31/5 62/5
Replace row 3 with -5/31 times row 3.
1 0 1/5 -7/5
0 1 -8/5 26/5
0 0 1 -2
Add -1/5 times row 3 to row 1.
1 0 0 -1
0 1 -8/5 26/5
0 0 1 -2
Add 8/5 times row 3 to row 2.
1 0 0 -1
0 1 0 2
0 0 1 -2
which translates back into:
x = -1
y = 2
z = -2
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