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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, Z1 Z2) and c(2,, z) = (c°,°, ), where c is a real number, is a vector space. Find the following vectors in P³. a) The zero vector. b) The negative of (3, 2, 1). c) The vector c(x, y, z), where c = d) The vector (2,3,1) + (3, 1, 2). and (x, y, z) = (9, 4, 36).

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, Z1 Z2) and c(2,, z) = (c°,°, ), where c is a real number, is a vector space. Find the following vectors in P³. a) The zero vector. b) The negative of (3, 2, 1). c) The vector c(x, y, z), where c = d) The vector (2,3,1) + (3, 1, 2). and (x, y, z) = (9, 4, 36).

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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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, Z1 Z2) and c(2,, z) = (c°,°, ), where c is a real number, is a vector space. Find the following vectors in P³. a) The zero vector. b) The negative of (3, 2, 1). c) The vector c(x, y, z), where c = d) The vector (2,3,1) + (3, 1, 2). and (x, y, z) = (9, 4, 36).
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, Z1 Z2) and c(2,, z) = (c°,°, ), where c is a real number, is a vector space. Find the following vectors in P³. a) The zero vector. b) The negative of (3, 2, 1). c) The vector c(x, y, z), where c = d) The vector (2,3,1) + (3, 1, 2). and (x, y, z) = (9, 4, 36).
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