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
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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plz solve question 9 with explanation ASAP
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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