Unformatted text preview: n
2
S ⊆ R , prove that (I − P ) = I − P , where I is the n × n identity matrix.
(b) (8 points) Give an example of a 3 × 3 matrix A whose columns are orthonormal and A
has exactly one entry equal to 0.
Solutions: (a) Since P is a projection matrix we know P 2 = P . So (I − P )2 = (I − P )(I −
P ) = I 2 − P I − IP − P 2 = I − 2P + P 2 = I − 2P + P = I − P .
(b) We’ll deal with the length 1 stuﬀ at the end. First we get the ‘ortho’ stuﬀ down. Let the
ﬁrst vector be in the xy plane. It’ll have third component equal to zero. So (1, 1, 0) will do.
The next vector has to be (a, b, c) where none of the entires are 0 and...
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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.
 Fall '05
 HUI
 Linear Algebra, Algebra, Vectors

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