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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![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.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F66fa70cb-bd96-49f7-bbde-9ceb23da10ec%2F71f01917-6dc0-4d15-bbf5-d94887de6b6c%2Fv6x5yvf_processed.png&w=3840&q=75)
Transcribed Image Text: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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