Question

Suppose that a system of linear equations has 3×5 augmented matrix whose 5th column is a pivot column. Is the system consistent? Explain.

Answer 1

No, the system is inconsistent.

Explanation:

If the last column is a pivot column, then that row gives an equation that looks something like 0x+0y+0z=1 , meaning , 0=1. Clearly, this is false.

So, the system of linear equations is inconsistent.