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## Homework Statement

Find the dimensions and basis of the following vector space V over the given feild K:

a) V is the set of all polynomials over R (real) of degree at most n and whose coefficients add to 0, K = R (real numbers)

b) K = R (real), and V is the set of functions from R to R which are solutions of the differential equation: d

^{2}f/dx

^{2}- 9f = 0

## Homework Equations

definition of basis, spanning and dimensions

## The Attempt at a Solution

for part a) i think the dimetions is N and the basis is all the factors

for part b) i think it has 2 dimentions and the basis is df/dx - 3 and df/dx +3