tut4 - Math 235 Tutorial 4 Problems 1: Determine which sets...

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Math 235 Tutorial 4 Problems 1: Determine which sets of vectors are orthonormal in R 3 under the inner product < ~x,~ y > = x 1 y 1 + 2 x 2 y 2 + 3 x 3 y 3 If a set is only orthogonal, normalize the vectors to produce an orthonormal set. a) 1 0 0 , 0 1 1 , 0 - 1 1 . b) 1 1 1 , 1 1 - 1 , - 2 1 0 . 2: Find the coordinates of ± 1 2 - 1 1 ² with respect to the orthonormal basis ³± 1 / 2 1 / 2 1 / 2 1 / 2 ² , ± 1 / 2 - 1 / 2 1 / 2 - 1 / 2 ² , ± - 1 2 0 1 2 0 ² , ± 0 1 2 0 - 1 2 ²´ in M 2 × 2 ( R ) under the inner product
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This note was uploaded on 11/28/2011 for the course MATH 235 taught by Professor Celmin during the Fall '08 term at Waterloo.

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