Problem: Given a matrix A, convert it to REF and RREF. Below shows how
to
convert the matrix A to RREF. To convert to REF (TODO). One reason to convert
Matrix \(A\) to its row echelon form, is to find the rank of \(A\). If matrix \(A\) is a \(4\times 4\), and when converted
to its row echelon form we find that one of the rows is all zeros, then the rank of \(A\) will be 3
and not full rank.
| Mathematica
Remove["Global`*"]
(mat={{1, 1, -2, 1},
{3, 2, 4, -4},
{4, 3, 3, -4}})//MatrixForm
|
\[ \left ( {\begin {array}{cccc} 1 & 1 & -2 & 1 \\ 3 & 2 & 4 & -4 \\ 4 & 3 & 3 & -4 \\ \end {array}} \right ) \] |
MatrixForm[RowReduce[mat]]
|
\[ \left ( {\begin {array}{cccc} 1 & 0 & 0 & 2 \\ 0 & 1 & 0 & -3 \\ 0 & 0 & 1 & -1 \\ \end {array}} \right ) \] |
| Matlab
clear all;
A=[1 1 -2 1
3 2 4 -4
4 3 3 -4];
rref(A)
|
ans =
1 0 0 2
0 1 0 -3
0 0 1 -1
|
| Maple
A:=Matrix([ [1,1,-2,1],[3,2,4,-4],[4,3,3,-4]]);
LinearAlgebra:-ReducedRowEchelonForm(A);
|
\[ \left [ {\begin {array}{cccc} 1&0&0&2\\ \noalign {\medskip }0&1&0&-3 \\ \noalign {\medskip }0&0&1&-1\end {array}} \right ] \] |