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  3. let a be a m × n matrix with entries in r. rec

Let A be a m × n matrix with entries in R. Recall that the...

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Advance Math

Let A be a m × n matrix with entries in R. Recall that the rowrank of A means the dimension of the subspace in RNspanned by the rows of A (viewed as vectors in Rn), andthe column rank means that of the subspace in Rm spannedby the columns of A (viewed as vectors in Rm).

(a) Prove that

n = (column rank of A) + dim S,

where the set S is the solution space of the homogeneousequation AX = 0, that is, S = {column vectors X : AX = 0} .

(b) Show that

row rank of A = column rank of A.

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