Math Help - Linear independence problem

1. Linear independence problem

Hello it's me again - need help again :|

here is the problem:

Find out if the vectors (2,1,1) (-1,0,1), (1,2,0) and (5,3,0) are linear independent. If they are linear dependent express one of them as linear combination of the rest.

2. Originally Posted by karagorge
Hello it's me again - need help again :|

here is the problem:

Find out if the vectors (2,1,1) (-1,0,1), (1,2,0) and (5,3,0) are linear independent. If they are linear dependent express one of them as linear combination of the rest.

First since you have 4 vectors in a three dimentional space what does that tell us?

3. that they are linear dependent?

4. Originally Posted by karagorge
that they are linear dependent?
Yes if you have more vectors than the dimention of your space they are always linearly dependant

Now just set up a 3 by 4 matrix with the above vectors as colums and solve for the dependacy constants.

5. Can you solve this equation?
$\left[ {\begin{array}{*{20}c} 2 & { - 1} & 1 \\ 1 & 0 & 2 \\ 1 & 1 & 0 \\ \end{array} } \right]\left[ {\begin{array}{*{20}c} \alpha \\ \beta \\ \gamma \\ \end{array} } \right] = \left[ {\begin{array}{*{20}c} 5 \\ 3 \\ 0 \\ \end{array} } \right]$