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Math521a exam2b sol

# Math521a exam2b sol - 2[30 pts In Zﬁsc use the Euclidean...

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Unformatted text preview: 2. [30 pts.] In Zﬁsc], use the Euclidean algorithm to write the greatest common divisor of 1:3 ~i— w + 1 and .732 + a: + 1 as a combinaiion of the two with polynomial ooeﬁcients. 3 3% " , ”é; g ta f 3" if? 3,32% 22“.} 333? 3 ﬂaw??? 3: WW “if 31%: i: W if if“ : 2 2" w y E i r W {:3 _;;> 9:. ax: wig ,_ v f?” by; w ; :5. [40 pts.] in this probiem you may assume that R is a commatative ring with identity, 1. (a) Let b E R and E61: T = {Tb 2 r E R}. Show that T is a subriﬁg of R. s 1%» Tami: 2M». :: wéw :, a?" :3 f” 1‘2. i; {in} W; a " WW. 1 w: 'v" : f , ii 7% .‘i‘ «we 2' M_ g 5 #- 1,»?4/ ml; L, “’— g} M. M m ,. f A \ ...
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