Consider A mXn matrix, The row vectors, r of A, r 1 = (a 11 .... a 1n ), .................... , r m = (a m1 ......... a mn ) The column vectors, c of A, The subspace span { r 1 ..... r m } of R n , where r 1 , ......., r m are the rows of the matrix A, is called the row space of A. The subspace span { c 1 , ...... , c n } of R m , where c 1, ....., c n are the columns of the matrix A, is called the column space of A. The solution space of the system of homogeneous linear equations Ax = 0 is called the nullspace of A. To find a basis for the row space of A, the row echelon form of A to be derived, and consider the non-zero rows that result from this reduction. These non-zero rows are linearly independent. To find a basis for the column space of A, the row echelon form of A to be derived, and consider the pivot columns that result from this reduction. These pivot columns are linearly independent, and that any non-piv...