Question

Needs a bit of help trying to figure out what it means to be a vector in C[0,1]

Answer 1

A vector in C[0,1] is a member of C[0,1]. I.e., a continuous function [0,1] --> R

Answer 2

So, I have the following choices to pick from, and there's more than an one right answer.

A. x^2
B. (infinity sign)
C. 2x^2 +5
D. x
E. 2x + 3
F. 1
G. sinx
H. 1/x
I. None of the above.

I picked, A C D E G, yet, the problem is wrong. Can you explain why? I'm pretty sure that all of the ones that I selected have at least two continuous derivatives. (The problem is actually, which of the following are vector spaces in C^2[0,1])

Answer 3

ACDEG are all correct, as is F

Answer 4

Ah... So any real numbers also count as continuous functions, that makes sense. B, infinity, wouldn't be correct, why?

Answer 5

Constant functions are also functions, yes. But infinity is not a real number, so f(x) = infinity is not the definition of a matrix.

Answer 6

Ohh okay. thanks! Problem solved :3

Answer 7

...definition of a FUNCTION. Sorry got matrices on the brain as I'm working a problem with them.

Answer 8

Ahaha, I know that feeling. S'all good.