# Linear independence problem

• May 4th 2011, 07:43 AM
karagorge
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.

• May 4th 2011, 07:47 AM
TheEmptySet
Quote:

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?
• May 4th 2011, 07:51 AM
karagorge
that they are linear dependent?
• May 4th 2011, 08:07 AM
TheEmptySet
Quote:

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.
• May 4th 2011, 08:08 AM
Plato
Can you solve this equation?
$\left[ {\begin{array}{*{20}c} 2 & { - 1} & 1 \\ 1 & 0 & 2 \\ 1 & 1 & 0 \\ \end{array} } \right]\left[ {\begin{array}{*{20}c} \alpha \\ \beta \\ \gamma \\ \end{array} } \right] = \left[ {\begin{array}{*{20}c} 5 \\ 3 \\ 0 \\ \end{array} } \right]$