co = () (0) ) b) = sin(a+b)), and roma) cos(ra) sin(ra) + = 3. Consider the set S = { (sin®): 0 € R} using the following

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Co 0 B Sin A B And Roma Cos Ra Sin Ra 3 Consider The Set S Sin 0 R Using The Following 1 (81.78 KiB) Viewed 38 times

co = () (0) ) b) = sin(a+b)), and roma) cos(ra) sin(ra) + = 3. Consider the set S = { (sin®): 0 € R} using the following "definitions" of + and .: (sin(a)) + (son (b) o Show that for all (%) e S, (1) + (6) = (-). (That is, (6) is the "zero" vector in this space). Hint: what's cos(0)? sin(0)? o Show that 2. (6) (6). • Show that < . () = (0) • The previous parts showed that į · 2: () = (). Conclude that S is not a vector space. What property of vector spaces is violated? = = . =