Originally Posted by

**sunneej** Hey, can you guys please help me out with two questions?

1. The following set is a spanning set for R^3.

S = {(1,2,-1),(0,3,4),(2,1,-6),(0,0,2)}

Find a subset of S that is a basis for R^3.

Mr F says: Remove one of the vectors that can be written as a linear combination of the other three vectors.

And,

2. Find a basis for the solution space V of the following linear system in four variables x1, x2, x3, x4:

x1+x2=0

-x2+3x3=0

Mr F says: Where does x4 appear in the above equations?? First you need to solve these two equations for x1, x2, x3. There are an infinite number of solutions. These solutions can be written in parametric form. Let $\displaystyle {\color{red}x_2 = t}$, say, where t can be any real number. You should be able to construct a basis from this solution .....

Thanks in advance for great help guys :-).