form a solution to
the given system for any choice of the free parameter(s)

−2x1+3x2+2x3=6

Question

form a solution to
the given system for any choice of the free parameter(s) 

−2x1+3x2+2x3=6

anonymous · Answer

Let $x_1$ and $x_2$ be your free parameters.

anonymous · Answer

First let $x_1=0, x_2=1$.  Then $$
-2(0)+3(1)+2x_3=6 \implies 3+2x_3=6\implies x_3=\frac 3 2= 1.5
$$So our first vector is $$
\mathbf v_0=\begin{bmatrix}0 \ 1 \ 1.5\end{bmatrix}
$$

anonymous · Answer

Then let $x_1=1, x_2=0$ and find the next vector.

Does that help so far?  @paki123

anonymous · Answer

Kind of. I'm not really sure what to do after. Wy did you make x1 = 0, and x2 =1?

anonymous · Answer

They can be anything you want them to be, but they need to be linearly independent.

anonymous · Answer

0,1 and 1,0 are orthogonal, so they are clearly linearly independent.

anonymous · Answer

Could i make them equal s1, and s2? Since the answe will have to be in that format?