$\displaystyle \begin{pmatrix}

4 &2 &0| &a1 \\

2 & 3 &2| &a2 \\

0 &2 &2| &a3

\end{pmatrix}$

i need to solve it find (x,y,z)

replace x y and z with expression of a1 a2 a3 and get the span of the image in some basis

but after doing somw row reduction i get a line of zeros equals some exprression

and here y is a free variable so i cant get expressiom of a1 a2 a3 of it

what to do?

i need only a1 a2 a3 reprentation

having free variables messes it up