Prelim 2 [Solutions]

Solution a the plane is a two dimensional subspace of

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Unformatted text preview: ctor in the plane from part (a), and a vector normal to that plane. Solution: (a) The plane is a two dimensional subspace of R3 . The vectors (1, 0, 1) and 10 (0, 1, 2) are independent and in the plane so they form a basis. Set A = 0 1 so the 12 projection matrix is −1 ￿ ￿ 10 ￿ ￿ 10 5 −2 1 1 101 101 0 1 2 2 . = −2 P = A(AT A)−1 AT = 0 1 012 012 6 12 12 1 25 −2 −5/6 −2 −5/6 −7/6 (b) P −2 = −2/6 so −2 = 2/6 + −14/6 is the sum we want. 1 1/6 1 1/6 7/6 3) For the questions below, just write the complete word ‘TRUE’ or ‘FALSE’ or leave it blank. No explanations are needed for this question only. A correct answer is worth...
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This note was uploaded on 01/30/2014 for the course MATH 2940 taught by Professor Hui during the Fall '05 term at Cornell.

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