09: Let (R. +..) be a ring of real numbers and (Max2 +..) is a ring of 2x2 matrices over R. Let f:R-Max such that f(a) n - (8Thena) fis an isomorphism.b) fis not one-to-one but onto homomorphism.c) fisa homomorphism but got onto and not one-to-one.d) F is one-to-one but not onto homomorphism.

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Answered: 09: Let (R.+..) be a ring of real…

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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Let (R,+..) be a ring of real numbers and (Max+..) is a ring of 2×2 matrices over R. Let f:R¬ such that (a)(). Then Ka) fis an isomorphism. b) fis not one-to-one but onto homomorphism. 5377 c) fis a homomorphism but not onto and not one-to-one. d) F is one-to-one but not onto homomorphism. Let f(x), g(x) € Z(x) such that f(x)=1+2x+3x² and g(x)=2+x² + 2x³. Then a) deg(f(x)g(x)) deg(f(x)) + deg(g(x)). Let V be a finite dimension vector space over a field F and S₁, S are subsets of V such that S, is a per subset of S₂ Then a) If S₂ be a basis for V then S, is a basis for V. b) If S, be a basis for V then Sy is a basis for V. c) If S, generate V then S, generate V. d) If Sa generate V then S₁ generate V.
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09: Let (R.+..) be a ring of real numbers and (M₁2+..) is a ring of 2x2 matrices over R. Let f: R Max such that f(a) n -(0 Then a) fis an isomorphism. b) fis not one-to-one but onto homomorphism. c) fisa homomorphism but got onto and not one-to-one. d) F is one-to-one but not onto homomorphism.