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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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 Fall '05
 HUI
 Linear Algebra, Algebra, Vectors

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