operations are defined, + and - . Two fields are {C; +, } and {R; +, ·} with the usual addition and multiplication operations. These fields are simply denoted by C and R. Another field is the field of rational functions with real coefficients R(s). (b) A subset of R(s) is the set of proper rational functions R,(s). Give a reason why {R,(8); +, ·} is not a field.
operations are defined, + and - . Two fields are {C; +, } and {R; +, ·} with the usual addition and multiplication operations. These fields are simply denoted by C and R. Another field is the field of rational functions with real coefficients R(s). (b) A subset of R(s) is the set of proper rational functions R,(s). Give a reason why {R,(8); +, ·} is not a field.
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:The definition of a field {F; +, } consisting of a set F with elements called scalars on which two
operations are defined, + and - Two fields are {C; +, } and {R; +, ·} with the usual addition and
multiplication operations. These fields are simply denoted by C and R. Another field is the field of
rational functions with real coefficients R(s).
(b)
A subset of R(s) is the set of proper rational functions R,(s). Give a reason
why {R,(s);+, '} is not a field.
|
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