201f05mt1[1]

# 201f05mt1[1] - B U Department of Mathematics Math 201...

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Unformatted text preview: B U Department of Mathematics Math 201 Matrix Theory Fall 2005 First 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 V be the subspace of R 4 spanned by the vectors: x = 1 1- 1 , y = 1 2 3 4 , z = 2 3 3 3 . Determine the dimension and find a basis for V . Solution: Note that x + y = z and y is not a multiple of x . It follows that { x, y } is a basis for V and dim V = 2. 2.) (a) Let A = 1 1 1 7- 1 2 . Determine A T and find A- 1 if it exists. Solution: A T = 1 1 7 1- 1 2 . To find the inverse, we apply Gauss-Jordan procedure 1 1 1 1 1 7- 1 2 1 - R 1 + R 2 → R 2- 7 R 1 + R 3 → R 3...
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201f05mt1[1] - B U Department of Mathematics Math 201...

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