This problem is #8 from pg. 84 of Hoffman & Kunze Linear algebra.
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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.