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Math Help - Rank of a matrix

  1. #1
    Member roshanhero's Avatar
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    Rank of a matrix

    What does the rank of a matrix tells about the consistency of the given equation?
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  2. #2
    Super Member Showcase_22's Avatar
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    I'm not sure what consistency is when applied to matrices, but here's something I knowabout ranks:

    The rank of a matrix is equal to the number of linearly independent equations in the system.
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  3. #3
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    A system of equations is "consistent" if there exist at least one solution to the system. If the rank of an n by n coefficient matrix is n, then there exist a unique solution and the system is consistent. If the rank is less than n, then the range of the matrix is a subspace or [itex]R^n[/itex] and there exist a solution if and only if the vector on the right hand side of the equation is in that subspace.
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