This problem is #8 from pg. 84 of Hoffman & Kunze Linear algebra.
Please see the attached file for the fully formatted problem.
You should have the appropriate definitions in your textbook(s) or lecture notes, however just in case here is a reference web page: http://en.wikipedia.org/wiki/Kernel_%28linear_operator%29
The null space of a linear ...
Linear Operators, Range and Null Space are investigated. The solution is detailed and well presented. The response was given a rating of "5/5" by the student who originally posted the question.