plz solve question 10 with explanation ASAP 09.Show that the set V = R, of all positive real numbers with operationsx + y = xy,a · x = xª,for x, y e V, a E Ris 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 theU = { 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

We have to show that the set V with the addition operation x1, y1+x2, y2=x13+x233, y13+y233 and…

Answered: 10. Show that V = R² with the standard…

10. Show that V = R² with the standard scalar multiplication, but addition defined by (x, , y.) + (x, , y2) = r + a?, /v? + v? is a vector space.

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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Question

plz solve question 10 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

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