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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(x, y, z) = (x, y, z), where c is a real number, is a vector space. Assuming that vectors u, p, q, and r are vectors in the space P3, write vector u = linear combination of vectors p = (1, 2, 2), q = (2, 1, 2), and r = (2,2,1). (1, 2) as a

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(x, y, z) = (x, y, z), where c is a real number, is a vector space. Assuming that vectors u, p, q, and r are vectors in the space P3, write vector u = linear combination of vectors p = (1, 2, 2), q = (2, 1, 2), and r = (2,2,1). (1, 2) as a

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 show¹ 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(®,y, z) = (r°,g°, ), where c is a real number, is a vector space. as a Assuming that vectors u, p, q, and r are vectors in the space P3, write vector u = (1, 2) as linear combination of vectors p = (1,2,2), q = (2,1,2), and r = (2,2,1).
Transcribed Image Text:Let P be the set of positive real numbers. One can show¹ 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(®,y, z) = (r°,g°, ), where c is a real number, is a vector space. as a Assuming that vectors u, p, q, and r are vectors in the space P3, write vector u = (1, 2) as linear combination of vectors p = (1,2,2), q = (2,1,2), and r = (2,2,1).
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