(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

find the rank and nullity of the linear transformation T:U -> V and find the basis of the kernel and the image of T

2. Relevant equations

U=R[x]<=5 V=R[x]<=5 (polynomials of degree at most 5 over R), T(f)=f'''' (4th derivative)

3. The attempt at a solution

Rank = 2

Nullity = 4

basis of kernel = {1,x,x^2,x^3} ?

since a kernel is mapped to V, then the image is the zero vectors? and the basis of the image of T is the empty set?

**Physics Forums | Science Articles, Homework Help, Discussion**

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Homework Help: Polynomials vector space

**Physics Forums | Science Articles, Homework Help, Discussion**