Suppose a system of linear equations has a 3 5 augmented matrix whose fifth column is a pivot column. is the system consistent? why (or why not) ? 4

The system will be inconsistent.

Step-by-step explanation:

We are given that a system of linear equations has a 3*5 augmented matrix whose fifth column is a pivot column.

Then such a system is not consistent because since the augmented matrix has a pivot in fifth column it means that the new column added to the matrix A will lead to increase in the rank as that of matrix A.

Hence the rank of A and Augment A will not remain same and hence the system will be inconsistent.