In computer science and mathematics, the row space of an m-by-n matrix with real entries is the subspace of Rn generated by the row vectors of the matrix. Its dimension is equal to the rank of the matrix and is at most min(m,n).
A basis for the rowspace are rows 1, 2, and 3 (taken as column vectors) of the reduced matrix.
The rowspace of A is simply the nonzero rows of the reduced form of A. Also, since A is 5x7 the dimension of the null space of A must be two (5+2=7).
Notice that the column space of A^{T} is the same as the rowspace of A. Similarly, the rowspace of A^{T} is the column sapce of A. The dimension of the column space of A^{T} equals five as there are five vectors in its basis, also, the rank is 5.
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