Answers to exercises LINEAR ALGEBRA - Joshua

LINEAR ALGEBRAJim HefferonThird editionAnswers to ,R+,Rnreal numbers, positive reals,n-tuples of realsN,Cnatural numbers{0,1,2,..}, complex numbers( ),[ ]open interval, closed interval .. sequence (a list in which order matters)hi,jrowiand columnjentry of matrixHV,W,Uvector spaces~v,~0,~0 Vvector, zero vector, zero vector of a spaceVPn,Mn mspace of degreenpolynomials,n mmatrices[S]span of a set B,D ,~ ,~ basis, basis vectorsEn= ~e1, ..,~en standard basis forRnV =Wisomorphic spacesM Ndirect sum of subspacesh,ghomomorphisms ( LINEAR maps)t,stransformations ( LINEAR maps from a space to itself)RepB(~v), RepB,D(h)representation of a vector, a mapZn morZ,In norIzero matrix, identity matrix|T|determinant of the matrixR(h),N(h)range space, null space of the mapR (h),N (h)generalized range space and null spaceGreek letters with pronounciationcharacternamecharactername alphaAL-fuh nuNEW betaBAY-tuh , xiKSIGH , gammaGAM-muhoomicronOM-uh-CRON , deltaDEL-tuh , piPIE epsilonEP-suh-lon rhoROW zetaZAY-tuh , sigm

Preface These are answers to the exercises in Linear Algebra by J Hefferon. An answer labeledhereasOne.II.3.4isforthequestionnumbered4fromthefirstchapter,second

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