Y2, 22) = c(x, y, z) = (cx, cy, 0) a vector space. X2, Y1 + Y2, Z1 + z2) %3! not a vector space because the associative property a not a vector space because it is not closed under scal not a vector space because the associative property c not a vector space because the multiplicative identity E) + (x2, Y2, z2) c(x, у, 2) - a vector space. (0, 0, 0) (cx, cy, cz) !3! = not a vector space because the commutative property s not a vector space because the additive identity prop s not a vector space because it is not closed under scal s not a vector space because the multiplicative identity (x1 + X2 + 5, Y1 + y2 + 5, z1 +2 z1) + (x2, Y2, z2) c(x, у, 2) sa vector space. (cx, cy, cz) is not a vector space because the additive identity prop is not a vector space because the additive inverse prop- is not a vector space because it is not closed under scal is not a vector space because the distributive property , z1) + (x2, Y2, Z2) = (x1 + X2 + 3, Y1 + Y2 + 3, z1 + (cx + 3c - 3, cy + 3c - 3, cz + %3! C(x, y, z) is a vector space. is not a vector space because the additive identity prop

Solution to this HW problem, please.

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Consider the set R²={(a,b)Da,b ER}. Suppose the following operations are defined on this set. Addition: (X 1.y 1)® (x 2Y2)=(x1+X2.Y1+Y2) • Scalar Multiplication: C © (x.y)=(cx,÷y) Which of the following axioms for a vector space fail to hold under these operations? O Distributivity of scalar multiplication over vector addition (c +d)O u=(c ©u)e (dO u) for all scalars C,d and all ordered pairs u=(x.y) 10 u=u for all u ER? O Closure under addition Additive identity QUESTION 15 Find the coordinates of X= (13, 26, 39) relative to the orthonormal basis B = inR 13 49 29 -78 O b.(x], =| 58 39 61 =| 58

Prove that "Let v1, v2 ER^n, V:= {sv1 + sv2 |5,t ER} is a vector space.