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The set is a vector space. O The set is not a vector space because the associative property of addition is not satisfied. The set is not a vector space because it is not closed under scalar multiplication. O The set is not a vector space because the associative property of multiplication is not satisfied. The set is not a vector space because the multiplicative identity property is not satisfied.

The set is a vector space. O The set is not a vector space because the associative property of addition is not satisfied. The set is not a vector space because it is not closed under scalar multiplication. O The set is not a vector space because the associative property of multiplication is not satisfied. The set is not a vector space because the multiplicative identity property is not satisfied.

Elementary Linear Algebra (MindTap Course List)
Elementary Linear Algebra (MindTap Course List)
8th Edition
ISBN:9781305658004
Author:Ron Larson
Publisher:Ron Larson
Chapter4: Vector Spaces
Section4.2: Vector Spaces
Problem 38E: Determine whether the set R2 with the operations (x1,y1)+(x2,y2)=(x1x2,y1y2) and c(x1,y1)=(cx1,cy1)...
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Rather than use the standard definitions of addition and scalar multiplication in R3, suppose these two operations are defined as follows. With these new definitions, is R3, a vector space? Justify your answers.
(a) (X1, Y1, z1) + (x2, Y2, z2) = (x1 + X2, Y1 + Y2, Z1 + Z2) c(x, y, z) = (cx, cy, 0) O The set is a vector space. The set is not a vector space because the associative property of addition is not satisfied. The set is not a vector space because it is not closed under scalar multiplication. The set is not a vector space because the associative property of multiplication is not satisfied. O The set is not a vector space because the multiplicative identity property is not satisfied.
Transcribed Image Text:(a) (X1, Y1, z1) + (x2, Y2, z2) = (x1 + X2, Y1 + Y2, Z1 + Z2) c(x, y, z) = (cx, cy, 0) O The set is a vector space. The set is not a vector space because the associative property of addition is not satisfied. The set is not a vector space because it is not closed under scalar multiplication. The set is not a vector space because the associative property of multiplication is not satisfied. O The set is not a vector space because the multiplicative identity property is not satisfied.
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