Math 294 Prelim 1 Spring 2005 Do ALL5 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 abAba=−, where 221+=. Find two nonzero perpendicular vectors vGand wGsuch that Avv=GGand Aww= −GG. (20pts) 1b Without doing any calculations, find1A−. Explain your reasoning. (5pts) 2a Decide whether the linear transformation yAx=GGdefined by 1123212331232349yxxxyxxxxx=++=+ +is invertible. Find the inverse transformation 1A−if it exist. (15pts) 2b An nby nsquare matrix Bhas 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)(5pts)3aFind the set Sof 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).