Thread: Consistency of a matrix

Hi guys,

My problem states:

Let be an augmented matrix of size m x m+1 (that is to say, the coefficient matrix of the system is square and of size m x m), and has all non-zero entires. Prove or disprove that this system is consistent and, in fact, has one and only one solution.

Any quick hints as to how to start this problem?

Thanks!
James

Originally Posted by james121515

Hi guys,

My problem states:

Let be an augmented matrix of size m x m+1 (that is to say, the coefficient matrix of the system is square and of size m x m), and has all non-zero entires. Prove or disprove that this system is consistent and, in fact, has one and only one solution.

Any quick hints as to how to start this problem?

Thanks!
James

If you are unsure whether or not a result is true, the best way to start is by experimenting with simple examples. In this case, take m=2, so that you are looking at 2x3 matrices. If such a matrix has all nonzero entries, does it necessarily represent a consistent system with only one solution?