# For a Matrix, what is a “Solution Vector”?

If given a value $N$ and told to generate the following:

• A random matrix $A[N][N]$
• A solution vector $S[N]$

What would be a "solution vector" of a randomly generated matrix? I am not sure I have heard the term used before or I am simply mixing terms in my mind.

• My hunch is that it S will either be the $x$ or the $b$ in the equation $Ax=b$. The word "solution" implies it may be more likely to be the $x$ You may be able to glean a little more information from the context it arises in. – David Reed Jan 13 '18 at 4:39
• @DavidReed So it would be appear that it would be the $x$; but can you derive $x$ upon generation of a random matrix? – pstatix Jan 13 '18 at 4:47
• It looks like they want you to use the same parameter to generate the x (viewing it as a 1 column matrix). You would not be able derive x without first having the b. – David Reed Jan 13 '18 at 5:06
• @DavidReed So mathematically you cannot solve for $x$ without having $b$ even though you have the matrix? – pstatix Jan 13 '18 at 16:27
• Yes, different values of b will give you different values of x – David Reed Jan 13 '18 at 16:45