This is documentation for Mathematica 3, which was
based on an earlier version of the Wolfram Language.
 RowReduce RowReduce[ m ] gives the row-reduced form of the matrix m. Example: RowReduce[ 3, 1, a , 2, 1, b ]. RowReduce performs a version of Gaussian elimination, adding multiples of rows together so as to produce zero elements when possible. The final matrix is in reduced row echelon form. If m is a non-degenerate square matrix, RowReduce[ m ] is IdentityMatrix[ m ]. If m is a sufficiently non-degenerate rectangular matrix with rows and more than columns, then the first columns of RowReduce[ m ] will form an identity matrix. RowReduce works on both numerical and symbolic matrices. RowReduce[ m , Modulus -> n ] performs row reduction modulo n. RowReduce[ m , ZeroTest -> test ] evaluates test [ m [[ i , j ]] ] to determine whether matrix elements are zero. See the Mathematica book: Section 3.7.8. See also Implementation NotesA.9.44.27MainBookLinkOldButtonDataA.9.44.27. See also: LinearSolve, Inverse, NullSpace, GroebnerBasis. Further Examples A non-singular matrix can be row-reduced to the identity matrix. In[1]:= Out[1]//MatrixForm= For non-zero singular matrices, the last row reduces to zero and the last column cannot be zeroed (if not zero from the start). In[2]:= Out[2]//MatrixForm= You can use RowReduce to solve a system of linear equations. This gives the solution to the linear system {x + y - z == 1, x + 2y + 5z == 1, 2x + y + 3z == -2}. In[3]:= Out[3]= Column 1 corresponds to the variable x, column 2 to the variable y and column 3 to the variable z. So the solution of the system is x = , y = , and z = .