Solve the following system of linear equations using
the Gauss-Jordan elimination method over the corresponding
augmented matrix. Each solution, if it
exists, must be expressed in vector form.
x + y + z + u + v + w = 10,
2x − y + 3z − u + v − w = 5,
x − 2y + z + u − v + 2w = 7,
3x + y − 2z + 4u − v − w = 12.
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