Thread: span of vectors

How do i prove that the following vectors span R3?

(1,1,0), (1,2,1), (4,6,2), (1,1,1)

I'd appreciate any help with this. Thanks.

Originally Posted by Louise

How do i prove that the following vectors span R3?
(1,1,0), (1,2,1), (4,6,2), (1,1,1)

Just show that these three are l.i.
(1,1,0), (1,2,1), (1,1,1)

I think i have to show spanning using guassian elimination, however because i have 3 equations and 4 unknowns i find an arbitrary solution for z.

What is the dimension of ?
We only need that many linearly independent vectors.

I know what you mean, the question asks to show that the vectors span R3 but are not linearly independent.

Originally Posted by Louise

I know what you mean, the question asks to show that the vectors span R3 but are not linearly independent.

Well of course they are not linearly independent. No four vectors in can be linearly independent.
But three from that set are linearly independent and threrfore span .
If any set spans the space, then by adding one more the set still spans the space.