Suppose the coefficient matrix of a system of linear equations has a pivot position in every row. Explain why the system is consistent?

If in each row of the supposed coefficient matrix, there is a pivot position. Therefore, it is true that the bottom row of the coefficient matrix also has a pivot position. As a result, there will not be space for the augmented column to have a. Thus, we say the system is consistent.

Step-by-step explanation:

In the problem, we have a coefficient matrix comprising linear equations. If in each row of the supposed coefficient matrix, there is a pivot position. Therefore, it is true that the bottom row of the coefficient matrix also has a pivot position. As a result, there will not be space for the augmented column to have a. Thus, we say the system is consistent based on the theorem.