Math 136Sample Term Test 2 # 1 AnswersNOTE: - Only answers are provided here (and some proofs). On the test youmustprovidefull and complete solutions to receive full marks.1.Short Answer Problemsa) What is the definition of a basis of a vector spaceV?
b) What is the definition of the dimension of a vector spaceV?
c) LetL:Rn→Rmbe a linear mapping. Prove thatL(~0) =~0.
d) State the definition of a vector spaceVoverR.