10 points Quiz 8 DUE: In class Wednesday, 4/30/14Name:Instructions: Do each problem correctly. To receive credit, you must also show allwork, and your work must be easy to read.1. Let W be a subspace of Rn. Prove W⊥is a subspace of Rn.(5 points)2. Diagonalize A ifA =0 1 11 0 11 1 0What are P and D to make A = P DP−1?(5 points)10 points Quiz 9 DUE: In class Wednesday, 4/30/14Name:Instructions: Do each problem correctly. To receive credit, you must also show allwork, and your work must be easy to read.3. If A is an n × n matrix, what is the orthogona l complement of Row ATand ColAT?(2 points)4. LetA =0 −1 11 0 21 1 1.Find (specifically!) a basis for each of the following sets:1. Nul A2. Nul AT3. Row A4. Col AVerify tha t Nul A and Row A are orthogonal complements of each other. Also, verifythat Nul ATand Col A are orthogona l complements of each other.(8
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