U = R³ w/ standard vector addition, but w/ scalar multiplication given by r(x, y, z) = (r²x, ry, rz) for (x, y, z) € R³ and r E R. Prove that U is not a vector space by the following distributive property: Let u = vector u For any u € V & real numbers r and s, (r +s) u = ru+su.

U = R³ w/ standard vector addition, but w/ scalar multiplication given by r(x, y, z) = (r²x, ry, rz) for (x, y, z) € R³ and r E R. Prove that U is not a vector space by the following distributive property: Let u = vector u For any u € V & real numbers r and s, (r +s) u = ru+su.

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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Question

U = R³ w/ standard vector addition, but w/ scalar multiplication given by r(x, y, z) = (r²x, ry, rz) for (x, y, z)
€ R³ and r E R. Prove that U is not a vector space by the following distributive property:
Let u = vector u
For any u EV & real numbers r and s, (r +s) u = ru+su.

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