SOLUTION: Solve the system: {{{3x-y+2z=3}}} {{{2x+3y-z=-3}}} {{{x-2y+3z=2}}} Thanks :)

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Question 442935: Solve the system:
3x-y%2B2z=3
2x%2B3y-z=-3
x-2y%2B3z=2
Thanks :)
Answer by swincher4391(1107) About Me  (Show Source):
You can put this solution on YOUR website!
We will start by making an augmented matrix.
matrix%283%2C4%2C3%2C-1%2C2%2C3%2C2%2C3%2C-1%2C-3%2C1%2C-2%2C3%2C2%29
Let's switch some rows so that we can get leading ones.
matrix%283%2C4%2C1%2C-2%2C3%2C2%2C3%2C-1%2C2%2C3%2C2%2C3%2C-1%2C-3%29
Multiply row 2 and row 3 by -1.
matrix%283%2C4%2C1%2C-2%2C3%2C2%2C-3%2C1%2C-2%2C-3%2C-2%2C-3%2C1%2C3%29
Notice we have leading ones now.


Multiply row 1 by 3 and add it to row 2
matrix%283%2C4%2C1%2C-2%2C3%2C2%2C0%2C-5%2C7%2C3%2C-2%2C-3%2C1%2C3%29
Multiply row 1 by 2 and add it to row 3
matrix%283%2C4%2C1%2C-2%2C3%2C2%2C0%2C-5%2C7%2C3%2C0%2C-7%2C7%2C7%29
Multiply row 3 by -1 and add it to row 2
matrix%283%2C4%2C1%2C-2%2C3%2C2%2C0%2C2%2C0%2C-4%2C0%2C-7%2C7%2C7%29
Divide row 2 by 2, and row 3 by 7.
matrix%283%2C4%2C1%2C-2%2C3%2C2%2C0%2C1%2C0%2C-2%2C0%2C-1%2C1%2C1%29
Multiply row 2 by 2 add it to row 1 ... also add row 2 to row 3.
matrix%283%2C4%2C1%2C0%2C3%2C-2%2C0%2C1%2C0%2C-2%2C0%2C0%2C1%2C-1%29
Multiply row 3 by -3 and add it to row 1.
matrix%283%2C4%2C1%2C0%2C0%2C1%2C0%2C1%2C0%2C-2%2C0%2C0%2C1%2C-1%29
x = 1, y = -2, z = -1.
Let's check:
3x + -y + 2z = 3(1) +2 -2 = 3
2x + 3y -z = 2(1) +3(-2) -(-1) = 2 -6 +1 = -3
x - 2y + 3z = 1 +4 -3 = 2
So yes, the solution works.