Homework Statement
Which of the following subsets of R3 are subspaces? The set of all vectors of the form (a,b,c) where a, b, and c are...
Homework Equations
1. integers
2. rational numbers
The Attempt at a Solution
I think neither are subspaces. IIRC, the scalar just needs to be...
Thanks for all the help. I usually end up coming here when I'm exhausted and frustrated, and then we see sloppy mistakes on my part. You're a tremendous help.
Whoops, yeah, two. Thank you for your help.
Oh, am I just wrong on the order of operations - the exponential would come first in kx^2, then multiplication by the scalar, which could leave us with negatives?
Oh, okay. So, for example
F(x)= x+1
G(x)= -x +1
Add them together and get a constant, 1. Is that correct?
If you have a moment, what was wrong with my original reasoning with F(x)=x^2
Homework Statement
Let V be the set of all nonconstant functions with operations of pointwise addition and scalar multiplication, having the real numbers as their domain. Is V a vectorspace?
Homework Equations
None.
The Attempt at a Solution
My guess is, no. For example
F(x) =...
Well, we start in R2 with the form (a,b2). Anything of the form (a,b2) that we can add to our original (a,b2) is going to leave us with a (a,b2). Any b in R2 that is squared is going to be positive, which doesn't leave us with a second element b2 that is negative and, subsequently, possessing...
Surely, Mark. Follow-up question: when you're checking to see if a subset of vectors is closed under scalar multiplication, must a scalar be within the original vector space from which the subset is derived?