In computer science and mathematics, the row space of an m-by-n matrix with real entries is the subspace of R^{n} 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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