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# Systems of Linear Equations : 3 Unknowns (Echelon Method)

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The problem is to find all the possible solutions to the following:

Eq 1: x + y = 2
Eq 2: y + z = 3
Eq 3: x + 2y + z = 5

I set up my matricies in the following:

1 1 0 2
0 1 1 3
1 2 1 5

operation 1: (-1*row 1 +row 3)

1 1 0 2
0 1 1 3
0 1 1 3

operation 2: (-1*row 2 +row 3)

1 1 0 2
0 1 1 3
0 0 0 0

operation 3: (-1*row 2 +row 1)

1 0 -1 -1
0 1 1 3
0 0 0 0

I am taking a optimization class, but I have never had linear algebra. From the review problems in the book, I have got this far, but I don't know what else I could do now operational wise that would make sense, and I don't know what this means to the solution. Can you help explain it to me?

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#### Solution Summary

Matrices are used to solve a system of equations.

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