Suppose that we try to solve the matrix equation AX = B by using an inverse matrix, but find that even though the matrix A is a square matrix, it has no inverse. What can be said about the outcome from solving the associated system of linear equations by the Gauss-Jordan method?

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Mathematics

Valentina Cisneros

30 July, 06:04

Suppose that we try to solve the matrix equation AX = B by using an inverse matrix, but find that even though the matrix A is a square matrix, it has no inverse. What can be said about the outcome from solving the associated system of linear equations by the Gauss-Jordan method?

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Answers (1)

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Lillie Conway · Answer 1

The system will be found to be inconsistent or dependent.

Step-by-step explanation:

The matrix A will have no inverse for two different reasons:

The system is inconsistent The system is dependent

In the latter case, the Gauss-Jordan method will find a set of parametric equations for a solution. In the former case, there is no solution.

The outcome will depend on the reason why there is no inverse.