
linear independence
Show that the following is linearly independent or express one of the vectors in the set as a linear combination of the others.
{[2,1],[3,2],[1,2]}
Ok, this is what I had:
C_1*V_1 + C_2*V_2+.....+C_N*V_N = 0
2C_1+3C_2+C_3=0
C_1+2C_2+2C_3=0
But the thing is that I can't figure out how to use the method of elimination here. Help?

Try multiplying the second row by 2, adding the first row to it, and storing the result in the second row.

I like to use a matrix. You can use the rref to find the linear combination if there is one.
$\displaystyle \displaystyle
\begin{bmatrix}2&3&1\\1&2&2\end{bmatrix}\Rightarro w \mbox{rref}=\begin{bmatrix}1&0&4\\0&1&3\end{bmatrix}$
$\displaystyle V_3=4V_1+3V_2$
Another thing to note is you have 3 vectors in $\displaystyle \mathbb{R}^2$.