midterm-sols1 - Math 235 Midterm Exam SOLUTIONS Problem 1[8...

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Math 235 Midterm ExamSOLUTIONSProblem 1.[8 points]Compute a basis for each of the four fundamental subspaces of the matrixA=12034-1-212200156.
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Problem 2.[6=3+3 points]In each part below, a vector spaceVand a function,·i:V×VRare given. Decidewhether,·iis an inner product onV. Prove that your answer is correct.(a)V=R2, withx1x2,y1y2=x1y1+ 51x1y2+ 51x2y1+x2y2.
(b)V=P2(R), withp(x), q(x)=p(0) +p(1) +p(2)q(0) +q(1) +q(2) .

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