Question

Anyone good with vector spaces?

Answer 1

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

Answer 2

...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?

Answer 3

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

Answer 4

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.

Answer 5

thanks a lot