# Homework Help: LINEAR ALGEBRA: A is a 4X4 matrix, b&c are in R^4, Ax=b has uniq. soln. - Does Ax=c?

1. Sep 16, 2006

### VinnyCee

Let $A$ be a 4 X 4 matrix, and let $\overrightarrow{b}$ and $\overrightarrow{c}$ be two vectors in $\mathbb{R}^4$. We are told that the system $A\,\overrightarrow{x}\,=\,\overrightarrow{b}$ has a unique solution. What can you say about the number of solutions of the system $A\,\overrightarrow{x}\,=\,\overrightarrow{c}$?

MY ANSWER:

The only way that the system $A\,\overrightarrow{x}\,=\,\overrightarrow{c}$ has a unique solution is if A is invertable.

A is to be invertable.

$A\,\overrightarrow{x}\,=\,\overrightarrow{c}$ has a unique solution.

But maybe the solution set $\overrightarrow{c}$ does not have a unique solution because A is not truely invertable?

Last edited: Sep 17, 2006
2. Sep 17, 2006

### Galileo

If Ax=b has a unique solution, what does that tell you about the matrix A?

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