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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?