Question

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

−2x1+3x2+2x3=6

Answer 1

Let \(x_1\) and \(x_2\) be your free parameters.

Answer 2

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 \[
\mathbf v_0=\begin{bmatrix}0 \\ 1 \\ 1.5\end{bmatrix}
\]

Answer 3

Then let \(x_1=1, x_2=0\) and find the next vector.

Does that help so far? @paki123

Answer 4

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

Answer 5

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

Answer 6

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

Answer 7

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