prelim1 - Math 294 Prelim 1 Spring 2005 Do ALL 5 problems....

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Math 294 Prelim 1 Spring 2005 Do ALL 5 problems. Justify all your answers. Points will be deducted for illegible writing. No calculators. No points will be awarded for unexplained answers . 1a Consider a matrix A of the form ab A ba = , where 22 1 + = . Find two nonzero perpendicular vectors v G and w G such that A vv = G G and A ww = − G G . (20pts) 1b Without doing any calculations , find 1 A . Explain your reasoning. (5pts) 2a Decide whether the linear transformation yA x = G G defined by 1123 21 2 3 31 2 3 23 49 yxxx yx x x x x =++ =+ + is invertible. Find the inverse transformation 1 A if it exist. (15pts) 2b An n by n square matrix B has two equal columns, is it invertible ? ( no credit will be given to a right answer but wrong reasoning; if any part of your reasoning is wrong, it is a wrong reasoning ) ( 5 p t s ) 3a Find the set S of all vectors that are perpendicular to
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This note was uploaded on 04/04/2008 for the course MATH 2940 taught by Professor Hui during the Spring '05 term at Cornell University (Engineering School).

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