Description
The system of linear equations has a unique solution. Find the solution using Gaussian elimination or Gauss-Jordan elimination.
2y | + | z | = | 8 | ||
x | + | y | = | 8 | ||
3x | + | 3y | − | z | = | 12 |
Explanation & Answer
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2y + z = 8
x + y = 8
3x + 3y - z = 12
First, we write the matrix and we use row operations.
0 2 1 8
1 1 0 8
3 3 -1 12
Exchange Row 2 and Row 1. R2 <---> R1
1 1 0 8
0 2 1 8
3 3 -1 12
New R3 = R3 - 3*R1
1 1 0 8
0 2 1 8
0 0 -1 -12
New R2 = 1/2R2
1 1 0 8
0 1 1/2 4
0 0 -1 -12
New R1 = R1 - R2
1 0 -1/2 4
0 1 1/2 4
0 0 -1 -12
New R3 = -1*R3
1 0 -1/2 4
0 1 1/2 4
0 0 1 12
New R1 = R1 + 1/2*R3 ; New R2 = R2 - 1/2*R3
1 0 0 10
0 1 0 -2
0 0 1 12
So finally, we would have:
(x , y, z) = (10, -2, 12)
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