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.

Printable View

- Oct 26th 2008, 05:56 AMLouisespan 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. - Oct 26th 2008, 08:23 AMPlato
- Oct 26th 2008, 08:38 AMLouise
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.

- Oct 26th 2008, 08:54 AMPlato
What is the dimension of $\displaystyle R^3$?

We only need that many linearly independent vectors. - Oct 26th 2008, 09:39 AMLouise
I know what you mean, the question asks to show that the vectors span R3 but are not linearly independent.

- Oct 26th 2008, 09:47 AMPlato
Well of course they are not linearly independent. No four vectors in $\displaystyle R^3$ can be linearly independent.

But three from that set are linearly independent and threrfore span $\displaystyle R^3$.

If any set spans the space, then by adding one more the set still spans the space.