# Spanning sets?

• Apr 15th 2009, 03:55 PM
paulrb
Spanning sets?
I'm confused about spanning sets...I can't find any information about them from my book and I must have forgotten going over it in class.

Here's the question:
"W is the subspace of R^4 consisting of all vectors of the form [a,b,a-b,a+c] where a, b, c are in R. Find a spanning set for W."

A spanning set is a set of vectors whose linear combination is the subspace W (is this correct?)

So would this be a spanning set?
{a[1,0,1,1], b[0,1,-1,0], c[0,0,0,1]}
• Apr 15th 2009, 08:44 PM
NonCommAlg
Quote:

Originally Posted by paulrb
I'm confused about spanning sets...I can't find any information about them from my book and I must have forgotten going over it in class.

Here's the question:
"W is the subspace of R^4 consisting of all vectors of the form [a,b,a-b,a+c] where a, b, c are in R. Find a spanning set for W."

A spanning set is a set of vectors whose linear combination is the subspace W (is this correct?)

So would this be a spanning set?
{a[1,0,1,1], b[0,1,-1,0], c[0,0,0,1]}

you're almost correct! the set of three vectors $\begin{bmatrix} 1 \\ 0 \\ 1 \\ 1 \end{bmatrix}, \ \begin{bmatrix} 0 \\ 1 \\ -1 \\ 0 \end{bmatrix}, \ \begin{bmatrix}0 \\ 0 \\ 0 \\ 1 \end{bmatrix}$ is a spanning set for $W.$ (it's clear that these three vectors are linearly independent. so $\dim W=3.$)