span of vectors

Printable View

• Oct 26th 2008, 05:56 AM
Louise
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.
• Oct 26th 2008, 08:23 AM
Plato
Quote:

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)
• Oct 26th 2008, 08:38 AM
Louise
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 AM
Plato
What is the dimension of \$\displaystyle R^3\$?
We only need that many linearly independent vectors.
• Oct 26th 2008, 09:39 AM
Louise
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 AM
Plato
Quote:

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 \$\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.