what are the rank conditions for consistency of a linear algebraic system?(adsbygoogle = window.adsbygoogle || []).push({});

my proffessor said that the coefficient matrix augmented with the column value matrix must have the same rank as the coefficient matrix for consistency of the system of equations. however does the term rank apply to rectangular matrices such as an augmented matrix? I if so how is it calculated also I would like to know how to deduce this condition by reasoning [the derivation].

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# What are the rank conditions for consistency of a linear algebraic system?

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