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201s02mt2

# 201s02mt2 - B U Department of Mathematics Math 201 Matrix...

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Unformatted text preview: B U Department of Mathematics Math 201 Matrix Theory Spring 2002 Second Midterm This archive is a property of Bo˘gazi¸ ci University Mathematics Department. The purpose of this archive is to organise and centralise the distribution of the exam questions and their solutions. This archive is a non-profit service and it must remain so. Do not let anyone sell and do not buy this archive, or any portion of it. Reproduction or distribution of this archive, or any portion of it, without non-profit purpose may result in severe civil and criminal penalties. 1. Let W be in the plane in R 3 defined by 2 x 1- x 2 + 4 x 3 = 0, ( x 1 , x 2 , x 3 ) ∈ R 3 (a) Find an orthonormal basis for W. (b) Determine the orthonormal comlement W ⊥ of W . Solution: (a) x ∈ W ⇔ x = x 2   1 2 1   + x 3  - 2 1   ⇒ a =   1 2   , b =  - 2 1   is basis for W. Let q 1 = a k a k , b = b- ( q T 1 b ) q 1 , q 2 = b k b k q 1 = 1 √ 5   1 2   , q 2 = 1 √ 105  - 8 4 5   { q 1 , q 2 } is an ON basis for W.Note that the answer is not unique; this just on of theis an ON basis for W....
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201s02mt2 - B U Department of Mathematics Math 201 Matrix...

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