Midterm_S16_soln - Math 235 Midterm Solutions Total 50...

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Math 235Midterm SolutionsTotal: 50 marks1.Short Answer Problemsa) AreP2(R) andR2isomorphic? Discuss why or why not.[1]
b) LetB={1-x,1 +x}be a basis forP1(R) and letL:P1(R)P1(R) be a linearmapping. If [L]B=13-21and [p(x)]B=21, then expressL(p(x)) in the forma+bx.[2]
c) SupposeVbe ann-dimensional vector space, andT:VVis a linear map defined byT(~v) =λ~v. Compute the kernel and the range ofT.[3](Hint: There are two cases, depending onλ.)
2.Prove thathp(x), q(x)i=p(-1)q(-1) + 3p(0)q(0) + 5p(1)q(1) defines an inner productonP2(R).[6]
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