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
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
Elementary Linear Algebra (MindTap Course List)
8th Edition
ISBN:9781305658004
Author:Ron Larson
Publisher:Ron Larson
Chapter4: Vector Spaces
Section4.2: Vector Spaces
Problem 41E: Rather than use the standard definitions of addition and scalar multiplication in R2, let these two...
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