Suppose that a matrix A is formed by taking n vectors from R^m as its columns.(adsbygoogle = window.adsbygoogle || []).push({});

a) if these vectors are linearly independent, what is the rank of A and what is the relationship between m and n?

is the rank the same as the dimension of the column space, or n, and m less than or equal to n?

b) if these vectors span R^m instead, what is the rank of A and what is the relationship between m and n?

is the rank m and m=n?

c) if these vectors form a basis for R^m, what is the relationship between m and n then?

is m=n?

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# Matrix rank math help

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