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201s03mt1

# 201s03mt1 - 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 2003 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 T : R 3 → R 3 be defined by T ( x, y, z ) = ( x + 2 y + z, x + y, 2 y + z ). a) (5pnts) Write down what we must show to prove that T is a linear transformation b) (5pnts) What is the matrix representing this transformation in the standard basis for R 3 . c) (10pnts) Show that T is non-singular and find its inverse transformation! Solution: a) Must show T ( α ( x 1 , y 1 , z 1 ) + β ( x 2 , y 2 , z 2 )) = αT ( x 1 , y 1 , z 1 ) +...
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201s03mt1 - B U Department of Mathematics Math 201 Matrix...

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