Math1231-assignment.docx - MATH1231 Assignment – Emre Davut...

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MATH1231 Assignment – Emre Davut InceQuestion 1:The functionT:R2→R3is defined byT(x1x2)=(4x15x1+5x24x2)for all(x1x2)R2Show thatTis linear.(x((.x2
MATH1231 Assignment – Emre Davut InceWe can conclude from this working out thatTsatisfies the scalar multiplication condition andsince the addition condition is also true we have proved thatTis linear.Question 2:Show thatS={xR4:8x15x2+4x3+5x4=0}Is a subspace ofR4R4is a known vector space that represents all real four dimensional vectors, therefore we mustshow the subsetShas a zero element and the subset is closed under vector addition as well asscalar multiplication in order to determine ifSis a subspace ofR4.To check if the zero element exists we must substitute the vector(0000)intoS.

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Term
Three
Professor
Mak
Tags
Vector Space, Emre Davut Ince

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