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Let P be the set of positive real numbers. One can show that the set P³ = {(x, y, z)|x, y, z € P} with operations of vector addition and scalar multiplication defined by the formulae (x1, y₁, 21) + (x2, Y2, Z₂) = (x1x2, Y1Y2, Z122) and c(x, y, z) = (x, y, zº), where c is a real number, is a vector space. Find the following vectors in P³. a) The zero vector. b) The negative of (2, 1, 3). c) The vector c(x, y, z), where c = d) The vector (2, 3, 1) + (3, 1, 2). and (x, y, z) = (4,9, 16).

Let P be the set of positive real numbers. One can show that the set P³ = {(x, y, z)|x, y, z € P} with operations of vector addition and scalar multiplication defined by the formulae (x1, y₁, 21) + (x2, Y2, Z₂) = (x1x2, Y1Y2, Z122) and c(x, y, z) = (x, y, zº), where c is a real number, is a vector space. Find the following vectors in P³. a) The zero vector. b) The negative of (2, 1, 3). c) The vector c(x, y, z), where c = d) The vector (2, 3, 1) + (3, 1, 2). and (x, y, z) = (4,9, 16).

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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Let P be the set of positive real numbers. One can show that the set P³ = {(x, y, z)|x, y, z € P} with operations of vector addition and scalar multiplication defined by the formulae (x₁, y₁, 21) + (x2, Y2, Z₂) = (x1x2, Y1Y2, Z122) and c(x, y, z) = (xº, y, zº), where c is a real number, is a vector space. Find the following vectors in P³. a) The zero vector. b) The negative of (2,1,3). c) The vector c(x, y, z), where c = d) The vector (2,3,1) + (3, 1, 2). and (x, y, z) = (4,9, 16).
Transcribed Image Text:Let P be the set of positive real numbers. One can show that the set P³ = {(x, y, z)|x, y, z € P} with operations of vector addition and scalar multiplication defined by the formulae (x₁, y₁, 21) + (x2, Y2, Z₂) = (x1x2, Y1Y2, Z122) and c(x, y, z) = (xº, y, zº), where c is a real number, is a vector space. Find the following vectors in P³. a) The zero vector. b) The negative of (2,1,3). c) The vector c(x, y, z), where c = d) The vector (2,3,1) + (3, 1, 2). and (x, y, z) = (4,9, 16).
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