I have never liked span questions, so I could use some help with this.

First, suppose that is a vector space over a field .

Now suppose satisfies . Prove that .

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- September 22nd 2010, 07:28 AMRuntyProve that span{x,y}=span{y,z}
I have never liked span questions, so I could use some help with this.

First, suppose that is a vector space over a field .

Now suppose satisfies . Prove that . - September 22nd 2010, 07:46 AMSwlabr
Take x over to the other side, y+z=-x, to see that (can you see why?)

Then, do it the other way! - September 23rd 2010, 04:41 AMHallsofIvy
Saying that v is in the span of x and y means v= ax+ by for some scalars a and b.

Since x+ y+ z= 0, x= -y- z so v= a(-y- z)+ by. - September 23rd 2010, 10:43 AMRunty
- September 23rd 2010, 11:36 AMRaoh
Hi :)

..it also means,

and are vectors. - September 24th 2010, 05:17 AMHallsofIvy