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Math Help - dimension

  1. #1
    Junior Member ibnashraf's Avatar
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    dimension

    Hi, i need some help in understanding the following question:

    Let V be the vector space of all 2x2 matrices over a field F. Show that V has dimension 4 over F.
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  2. #2
    MHF Contributor alexmahone's Avatar
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    Re: dimension

    Try to find a basis for V.
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  3. #3
    Junior Member ibnashraf's Avatar
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    Re: dimension

    Quote Originally Posted by alexmahone View Post
    Try to find a basis for V.
    ok, to find a basis for V, i must show that it is linearly independent and that it spans the vector space.

    but where and how do i start to do this?
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  4. #4
    MHF Contributor alexmahone's Avatar
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    Re: dimension

    Quote Originally Posted by ibnashraf View Post
    ok, to find a basis for V, i must show that it is linearly independent and that it spans the vector space.

    but where and how do i start to do this?
    How about four 2x2 matrices, each with one 1 (at each position) and three 0's?
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