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

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Mathematics

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16 October, 01:10

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

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Broderick · Answer 1

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.