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Math Help - Dimension of a subspace

  1. #1
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    Dimension of a subspace

    A vector space of 2x2 Matrices with real entries, and let A be a subspace defined by

    Dimension of a subspace-codecogseqn.gif.

    How would you go about finding the dimension of A?
    (The question I'm looking at does have real entries, but I just want the general idea).

    I've missed the lecture on this, but my attempt is to show that they are linearly independent. If they are linearly independent then they form a basis. Then writing it out in a reduced row-echelon form and any rows that do not contain a leading coefficient are redundant and the dimension of A would be the number of rows that do contain a leading coefficient.
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  2. #2
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    Re: Dimension of a subspace

    Well, the dimension is bounded (above) by 3, so that limits the possibilities. I would want to work straight from the definition of linear independence.

    Here is a "trick" that may help: each matrix can be regarded as a 4-vector, so determine the LI in $\mathbb{R}^4$ of:

    {(a,b,c,d),(e,f,g,h),(i,j,k,l)}.
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