## anonymous 5 years ago Anyone good with vector spaces?

1. anonymous

a collection of vectors that contains theta must be linearly dependent. Thus theta cannot be contained in a basis. How do you go about proving this? I know that

2. anonymous

...I know that to be linearly dependent there must be scalars that are not zero in the collection of vectors, Does theta mean zero, or some sort of value?

3. anonymous

...theta is also zero...and the collection of vectors must = zero in the end

You have to prove some axioms regarding vector spaces. Suppose you had $\{R^2= <x,y> | x,y \in R\}$ Define Addition as: $<x_1,y_1> + <x_2,y_2> = <x_1+x_2,y_1+y_2>$ Then: $<x_1,y_1> + <x_2,y_2> = <x_1+x_2,y_1+y_2>=<a,b>$ $\in R= <x,y>$ Therefore, closed under addition, since the addition of two elements = an element inside $R^2$. Rinse and repeat for the other ones.

5. anonymous

thanks a lot