Reading Question A.1.2. Consider the equivalence relation on R² given by: ỹ + ||x|| = ||J||. Select all that apply. (a) For every vector , we have -I (b) The equivalence class of a vector i consists of +ĩ. Namely: [] = {x, –x} (c) The equivalence class of a vector i consists of the circle centerered at the origin of radius ||||. (d) The map T: R20 → R2/ ~, r [X,] where , := (r,0) is a bijection between the set of non-negative real numbers and the quotient set R?/ ~.

Advanced Engineering Mathematics
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ISBN:9780470458365
Author:Erwin Kreyszig
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Chapter2: Second-order Linear Odes
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Reading Question A.1.2. Consider the equivalence relation on R² given by: 7 ~ j
Select all that apply.
||x|| = ||||.
(a) For every vector , we have i ~ -
(b) The equivalence class of a vector i consists of +x. Namely: [x] = {x, –x}
(c) The equivalence class of a vector i consists of the circle centerered at the origin of radius || || .
(d) The map
T: R>0 → R/ ~, r> [x,]
where x,
set R2/ ~.
(r,0) is a bijection between the set of non-negative real numbers and the quotient
Transcribed Image Text:Reading Question A.1.2. Consider the equivalence relation on R² given by: 7 ~ j Select all that apply. ||x|| = ||||. (a) For every vector , we have i ~ - (b) The equivalence class of a vector i consists of +x. Namely: [x] = {x, –x} (c) The equivalence class of a vector i consists of the circle centerered at the origin of radius || || . (d) The map T: R>0 → R/ ~, r> [x,] where x, set R2/ ~. (r,0) is a bijection between the set of non-negative real numbers and the quotient
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