I've worked through the axioms, and have found that all of them hold apart from two in the case of a<2.
These two are:
There exists a zero vector such that f(x) + 0(x) = f(x) which can't work for a>2, since no zero function can exists as f(x) = (+ve integer)x + b
And that for any f(x), there...
Question: Show that the set of all functions of the form f(x) = ax+b, with a and b real numbers forms a vector space, but that the same set of functions with a > 2 does not.
Equations: the axioms for vector spaces
Attempt:
I think that the axiom about the zero vector is the one I need to use...
I've been given this question as an example of what I'll be facing next year. It's really daunting not having questions with specific steps for the first time!
I was thinking that I would have to somehow show that at a limit near to 2/3, there is a point where the Earth's crust above is much...
Homework Statement
The value of g measured at the bottom of a mineshaft is higher than that measured at the surface. Show that this implies the density of the Earth’s crust is less than 2/3 that of the mean density of the Earth.
Homework Equations
g(r) = -GM(r)/r^2
G = 6.67384 × 10-11...