# Consistency of a matrix

• Apr 18th 2011, 04:23 PM
james121515
Consistency of a matrix
Hi guys,

My problem states:

Let \$\displaystyle A\$ 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 \$\displaystyle A\$ 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
• Apr 18th 2011, 11:52 PM
Opalg
Quote:

Originally Posted by james121515
Hi guys,

My problem states:

Let \$\displaystyle A\$ 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 \$\displaystyle A\$ 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?