Matrice, solving the system, need to put it in right form!

[mr_coffee]

Hello everyone I had this system:
-2x1 + x2 = 5
6x1 - 3x2 = -15
$$\left( {\begin{array}{*{20}c} {-2} & 1 & 5 \\ 6 & -3 & {-15}\\ \end{array} } \right)$$

I then solved it down too:
$$\left( {\begin{array}{*{20}c} {-2} & 1 & 5 \\ 0 & 0 & 0\\ \end{array} } \right)$$

It wants me to put it parametric form:
so i did the following:
-2x1 + x2 = 5
2x1 = -5 + x2
x1 = (-5+x2)/2
let x2 = s;
[-5/2] + [1/2] S
[0 ] [0 ]

but its wrong! any ideas? Thanks

 

[TD]

You have to be careful, when you let $x_2 = s$, it doesn't just disappear/become zero. You still have then:

$$\left\{ \begin{gathered} x_1 = \frac{{ - 5 + x_2 }} {2} \hfill \\ x_2 = x_2 \hfill \\ \end{gathered} \right. \Leftrightarrow \left\{ \begin{gathered} x_1 = \frac{1} {2}s - \frac{5} {2} \hfill \\ x_2 = s \hfill \\ \end{gathered} \right$$

Can you get the correct vector-notation now?

 

[mr_coffee]

awsome, thanks again TD!

 

[TD]

No problem