T: M2x2 (R) → R2 [x] is given by r(; ;) a С 3 (а +ь+с+d) + (а+ 2b + 3с + 4d)ӕ + (а + 36 + 5с + 7d) a? Which statement about T is correct? O Tis neither onto nor one-to-one O Tis an isomorphism O Tis onto but not one-to-one O Tis one-to-one but not onto

T: M2x2 (R) → R2 [x] is given by r(; ;) a С 3 (а +ь+с+d) + (а+ 2b + 3с + 4d)ӕ + (а + 36 + 5с + 7d) a? Which statement about T is correct? O Tis neither onto nor one-to-one O Tis an isomorphism O Tis onto but not one-to-one O Tis one-to-one but not onto

Elements Of Modern Algebra

8th Edition

ISBN:9781285463230

Author:Gilbert, Linda, Jimmie

Publisher:Gilbert, Linda, Jimmie

Chapter6: More On Rings

Section6.2: Ring Homomorphisms

Problem 12E: 12. Consider the mapping defined by . Decide whether is a homomorphism, and justify your decision.

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Question

T: M2x2 (R) → R2 [x] is given by
r(; :)
a
T
С 3 (а +ь+с+d) + (а+ 2b + 3с + 4d)ӕ + (а + 36 + 5с + 7d) a?
Which statement about T is correct?
O Tis neither onto nor one-to-one
O Tis an isomorphism
O Tis onto but not one-to-one
O Tis one-to-one but not onto

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