Question

let v=(t,-3t) for t in R and let addition and scalar multiplication be the standard operations on vectors. determine whether v is a vector space.

Answer 1

I think you just have to check if: \[
\mathbf v(x)+\mathbf v(y)=\mathbf v(x+y)
\]And if \[
c\mathbf v(x)=\mathbf v(cx)
\]

Answer 2

so one of those will not check out and equal each other? thus it is not a vector space?

Answer 3

v=(t.-3t) is column vector i just didnt know how to type it as a column vector
\[\left(\begin{matrix}t \\ -3t\end{matrix}\right)\]

Answer 4

It doesn't look like it should be a vector space. v is R (one dimensional) and it has components t and -3t which are dependent on one another. I do not think scaling and adding will be supported

Answer 5

I'm taking lin aglebra now but have not done proofs, so you should get a second opinion

Answer 6

Just trying drawing the vector! Its impossible without two lines

Answer 7

thats what i thought at first that since t is in R and not R^2 that it would not be a vector space since V is t and -3t which that should be in R^2

Answer 8

I hope I understood the question correctly :-/

Answer 9

yup thats my logic too!

Answer 10

what do you mean by drawing the vector and it being impossible without two lines?