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09. Show that the set V = R of all positive real numbers with operations x + y = xy, a · x = xª, for x, y E V, a E R is a vector space. 10. Show that V = R² with the standard scalar multiplication, but addition defined by

09. Show that the set V = R of all positive real numbers with operations x + y = xy, a · x = xª, for x, y E V, a E R is a vector space. 10. Show that V = R² with the standard scalar multiplication, but addition defined by

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
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plz solve question 9 with explanation ASAP
09. Show that the set V = R, of all positive real numbers with operations x + y = xy, a · x = xª, for x, y e V, a E R is a vector space. 10. Show that V = R² with the standard scalar multiplication, but addition defined by (1, , y.) + (#, , y,) = ( +=, /v? + v?) is a vector space. Let P, be the set real polynomials of degree less than or equal to 2. following subsets are subspaces of P, ? 11. Which of the U = { p(x) € P, p(1) = p'(0) } b. v={ p(2) € P, | p(2) =r°(1) } а. W = { p(x) € P, max{p(0), p(1)} = 0 } X = { p(x) € P, max{ \p(0)| , \p(1)|} = 0 } с. d. 2
Transcribed Image Text:09. Show that the set V = R, of all positive real numbers with operations x + y = xy, a · x = xª, for x, y e V, a E R is a vector space. 10. Show that V = R² with the standard scalar multiplication, but addition defined by (1, , y.) + (#, , y,) = ( +=, /v? + v?) is a vector space. Let P, be the set real polynomials of degree less than or equal to 2. following subsets are subspaces of P, ? 11. Which of the U = { p(x) € P, p(1) = p'(0) } b. v={ p(2) € P, | p(2) =r°(1) } а. W = { p(x) € P, max{p(0), p(1)} = 0 } X = { p(x) € P, max{ \p(0)| , \p(1)|} = 0 } с. d. 2
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