201s06mt1 - B U Department of Mathematics Math 201 Matrix...

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B U Department of Mathematics Math 201 Matrix Theory Spring 2006 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-proFt 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-proFt purpose may result in severe civil and criminal penalties. 1. By Gauss-Jordan method compute the inverse of A = 0100 1010 0101 0010 , if exists. (12 points). Solution: . . .1000 . . .0100 . . .0010 . . .0001 −−−−−−−−−−−−−−−−−−→ r 1 r 2 , ( 1) r 2 + r 3 r 3 . . . . 0001 . . . . . −−−−−−−−−−−−→ ( 1) r 4 + r 1 r 1 1000 . . .010 1 . . . . . 101 0 . . −−−−−→ r 3 r 4 . . 1 . . . . . . . So the second part of the last matrix is A - 1 = 010 1
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2. Given a 3 × 3 matrix A = 500 150 015 , for which vectors X does there exist a scalar c such that AX = cX ?(13po in t s ) Solution: AX = x 1 x 2 x 3 = c x
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This note was uploaded on 11/16/2011 for the course MATH 201 taught by Professor Soysal during the Fall '08 term at Boğaziçi University.

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201s06mt1 - B U Department of Mathematics Math 201 Matrix...

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