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Solutions of the system of equations

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Determine the solutions of the system of equations whose matrix is row equivalent to
1 0 −1 |1
0 1 3 |1
0 0 0 |0
Give three examples of the solutions. Verify that your solutions satisfy the original system of equations.

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This solution is comprised of a detailed explanation to determine the solutions of the system of equations whose matrix is row equivalent to.

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The corresponding linear system with respect to the matrix is:
x-z=1
y+3z=1
Since we have three variables x,y,z and only two equations, ...

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