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Systems of Equations : Triangular Form and Matrices

Please give step by step instructions and name each step like triangular form, augmented matrix etc so I know when and what to do and can understand it. We are not using calculator so the steps need to be shown to the solution.

1) The augmented matrix of a linear system has been transformed by row operations into the form below. Determine if the system is consistent.

1 5 2 -6
0 4 -7 2
0 0 5 0

2) Is (3,4,-2) a solution of the following system?

5xsub1 - xsub2 +2xsub3 = 7
-2xsub1 + 6xsub2 +9xsub3 = 0
-7xsub1 + 5xsub2 -3xsub3 = -7

3) For what values of h and k is the following system consistent?

2xsub1 - xsub2 = h
-6xsub1 +3 xsub2 = k

Solution Preview

1. The corresponding linear system is
Then we get z=0, y=0.5 and x=-8.5
So we get a unique solution ...

Solution Summary

Questions involving systems of equations, matrices and consistency are concisely answered.