Showing nonsingular matrix has a unique solution

[bonfire09]

Homework Statement

It states that for any linear system with a nonsingular matrix of coefficients has solution and its solution is unique.

Homework Equations

The Attempt at a Solution

I wanted to put an diagram of an arbitrary nxn matrix showing it has unique solution but I'm not sure how to represent a nxn matrix in echelon form?

 

[bmb2009]

correct...The problem says (i think which you are trying to prove) that it has a solution and the solution is unique. So you know that the matrix of the arbitrary nxn matrix will have a pivot and ever row and column. To represent that use the given that it is a linear system with nonsingular matrix of coefficients. I've never seen the description as "non singular" before but I assume it relates to the fact that the matrix will be isomorphic to r^n

 

[bonfire09]

Oh ok. I assume its OK to use explain it using the assumption the matrix is nonsingular(means it has at one solu ion).