Problem 6. Let -oo and oo denote two distimct objects, neither of which is in R. Define an addition and scalar multiplication on RU{x}U{-x}. Specifically, the sum and product of two real numbers is as usual, and for t e R define if t <0 if t 0 if t 0, if t < 0 if t 0 if t> 0, 00 too = t(-0x) +t= 0, t+(-x)= -0+t%3D-x, (-x) + (-∞x) = -0, t+ o0 x + (-x) = 0. Determine whether RU{x}U{-x} is a vector space over R.
Problem 6. Let -oo and oo denote two distimct objects, neither of which is in R. Define an addition and scalar multiplication on RU{x}U{-x}. Specifically, the sum and product of two real numbers is as usual, and for t e R define if t <0 if t 0 if t 0, if t < 0 if t 0 if t> 0, 00 too = t(-0x) +t= 0, t+(-x)= -0+t%3D-x, (-x) + (-∞x) = -0, t+ o0 x + (-x) = 0. Determine whether RU{x}U{-x} is a vector space over R.
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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Transcribed Image Text:Problem 6. Let -oo and oo denote two distinct objects, neither of which
is in R. Define an addition and scalar multiplication on RU{x} U{-x}.
Specifically, the sum and product of two real numbers is as usual, and for t e R
define
if t <0
if t 0
if t>0,
if t <0
if t = 0
00
too D
t(-x)
0.
if t 0,
8.
t+ oo
+t-x, t+(-x) = 00+t=-o,
(-0x) + (-x) =-00, x + (-x) = 0.
Determine whether RU{ox}U{-x} is a vector space over R.
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