Answer 15 235_sample_mid_winter_2_soln - Math 235 Sample...

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Math 235Sample Midterm 2 AnswersNOTE: - Only answers are provided here (and some proofs). On the test youmustprovidefull and complete solutions to receive full marks.1.Short Answer Problemsa) Give the definition of an inner producth,ion a vector spaceV.
c) Give the definition of an orthogonal matrix.
d) Write a basis for the four fundamental subspaces ofA=0
2.LetVbe ann-dimensional vector space, and letT:VVbe defined byT(~v) =λ~vfor all~vinV, whereλRis a constant.a) Prove thatTis linear.
b) Compute the kernel and the range ofT. There are two cases, depending onλ.

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