# Math Help - linear independence

1. ## 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?

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

3. I like to use a matrix. You can use the rref to find the linear combination if there is one.

$\displaystyle
\begin{bmatrix}2&3&1\\1&2&2\end{bmatrix}\Rightarro w \mbox{rref}=\begin{bmatrix}1&0&-4\\0&1&3\end{bmatrix}$

$V_3=-4V_1+3V_2$

Another thing to note is you have 3 vectors in $\mathbb{R}^2$.