SOLUTION: solve the augmented matrix for a three-equation system in three unknowns x, y, z. 3 1 -2: 10 0 2 -3: 4 0 0 1: 4

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Question 463770: solve the augmented matrix for a three-equation system in three unknowns x, y, z.
3 1 -2: 10
0 2 -3: 4
0 0 1: 4
Answer by robertb(5830) About Me  (Show Source):
You can put this solution on YOUR website!
Proceed with Gauss-Jordan reduction:
%28matrix%283%2C4%2C3%2C+1%2C-2%2C+10%2C0%2C++2%2C++-3%2C++4%2C0+%2C++0%2C+++1%2C++4%29%29
~%28matrix%283%2C4%2C3%2C+1%2C-2%2C+10%2C0%2C++2%2C++0%2C+16%2C0+%2C++0%2C+++1%2C++4%29%29, by 3R3 + R2
~%28matrix%283%2C4%2C3%2C+1%2C0%2C+18%2C0%2C++2%2C++0%2C+16%2C0+%2C++0%2C+++1%2C++4%29%29, by 2R3 + R1
~%28matrix%283%2C4%2C3%2C+1%2C0%2C+18%2C0%2C++1%2C++0%2C+8%2C0+%2C++0%2C+++1%2C++4%29%29, R2/2
~%28matrix%283%2C4%2C3%2C+0%2C0%2C+10%2C0%2C++1%2C++0%2C+8%2C0+%2C++0%2C+++1%2C++4%29%29, by -R2 + R1
~%28matrix%283%2C4%2C1%2C+0%2C0%2C+10%2F3%2C0%2C++1%2C++0%2C+8%2C0+%2C++0%2C+++1%2C++4%29%29, by R1/3
Therefore, x = 10/3, y = 8, and z = 4.