Is this the correct method for finding a coordinate vector?

[Ted123]

Homework Statement

[PLAIN]http://img25.imageshack.us/img25/3409/linearf.jpg

Homework Equations

The Attempt at a Solution

Is this the right method to do this type of question (as I haven't seen an example of finding a coordinate vector before)?

Do I solve the following system of equations?

$\displaystyle \frac{1}{2} = x + \frac{1}{2}y + \frac{1}{3}z$

$\displaystyle \frac{1}{3} = -x + \frac{1}{2}y$

$\displaystyle -\frac{9}{2} = x+z$

If so by Guassian Elimination I get

$x=1,\,y=\frac{8}{3},\,z=-\frac{11}{2}$

So is $\begin{bmatrix} 1 \\ 8/3 \\ -11/2 \\ \end{bmatrix}$ the coordinate vector?

 

[tiny-tim]

Hi Ted123!

Yes, that's fine! ​