Question

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

Answer 1

If the fifth column of an augmented matrix, representing a system of linear equations, is a pivot column, the system is inconsistent as it implies a contradiction.

Step-by-step explanation:

If a system of linear equations is represented by an augmented matrix and the fifth column is a pivot column, this indicates that there is a leading entry (i.e., a pivot) in the last column, which typically corresponds to the constants in the equations. In the context of systems of equations, a pivot in the last column of the augmented matrix signifies that the system is inconsistent. This is because there would be a row that essentially states that a non-zero value is equal to zero, which is a contradiction. Consequently, no solution set can satisfy the system of equations.

Answer 2

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.