4. In each of the following, determine whether the indi- cated addition and scalar multiplication of ordered triples of real numbers yields a vector space. For those that are not vector spaces, determine which properties of a vector space fail to hold. a) (x1, VI , Z1) + (X2, )2, Z2 ) = (x1 + x2, y1 + y2, Z1 + Z2), c(x, y, z) = (cx, y, cz) b) (x1 , y1 , Z1 ) + ( X2, y2, Z2 ) = (z1 + Z2, )1 + )2, X1 + x2), c(x, y, z) = (cx, cy, cz) c) (x1 , y1 , Z1 ) + (X2, 12, Z2 ) = (x1 + x2, y1 + )2 - 2, z1 + Z2), c(x, y, z) = (cx, y, z)7. Let C denote the set of all convergent Sequences of real numbers {an}. Is C a vector space under the addition and scalar multiplication {an} 'l' {bit} = {an + bra}: Clan: = {can}? If not, why not