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Math Help - 2X2 matrices under addition using FHT

  1. #1
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    2X2 matrices under addition using FHT

    From earlier proofs, I know that the map tr: Mat2(R)-->R is a homomorphism and that the kernel of tr is defined by Ker(tr):={A is an elt of Mat2(R) such that A=2X2 identity matrix}.

    Now I'm having trouble using the Fundamental Homomorphism Theorem to determine that Mat2(R)/Ker(tr) as a factor group.

    Any help would be appreciated Thank you!
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  2. #2
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    Quote Originally Posted by Tracey21 View Post
    From earlier proofs, I know that the map tr: Mat2(R)-->R is a homomorphism and that the kernel of tr is defined by Ker(tr):={A is an elt of Mat2(R) such that A=2X2 identity matrix}.

    Now I'm having trouble using the Fundamental Homomorphism Theorem to determine that Mat2(R)/Ker(tr) as a factor group.

    Any help would be appreciated Thank you!
    the map \text{tr} is obviously onto and so your factor group is isomorphic to \mathbb{R}.
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