# Answer to Question #45471 in Abstract Algebra for jasvinder

Question #45471

The map f : R[x] -> M(subscript3)(R) is defined by

f ( a(subscript 0) + a(subscript 1)x + a(subscript 2)x(power 2) + ....... + a(subscript n)x(power n)

_ _

| a(subscript 0) a(subscript 1) a(subscript 2) |

= | 0 a(subscript 0) a (subscript 1) |

|_ 0 0 a(subscript 0) _|

Show that f is a group homomorphism.Determine ker(f) also.

f ( a(subscript 0) + a(subscript 1)x + a(subscript 2)x(power 2) + ....... + a(subscript n)x(power n)

_ _

| a(subscript 0) a(subscript 1) a(subscript 2) |

= | 0 a(subscript 0) a (subscript 1) |

|_ 0 0 a(subscript 0) _|

Show that f is a group homomorphism.Determine ker(f) also.

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