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={x∈R4:8x1−5x2+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.