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Math Help - linear systems

  1. #1
    Junior Member
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    linear systems

    G(t) is nxn matrix dependent on t. show solutions of x' = G(t)x form an n-dim subspace of the space of functions C^1(R^+,R^n) .

    Not sure how to do this.
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  2. #2
    Super Member Rebesques's Avatar
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    Ofcourse, G has to be continuous, or else x might not be C^1.


    Consider the n (unique) solutions to the n problems \{x_i'=Gx_i, \ x(0)=e_i\}_{1\leq i\leq n}, where \{e_i\} are the standard basis vectors.
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