Matrix Size & Validation
What is Vector?
Vector Scalar Multiple
Vector Inner Product
Vector Outer Product
Vector Cross Product
Vector Triple Cross Product
Vector Triple Dot Product
Scalar Triple Product
Orthogonal & Orthonormal Vector
Cos Angle of Vectors
Scalar and Vector Projection
What is a matrix?
Matrix Diagonal Is Diagonal Matrix?
Matrix Basic Operation
Is Equal Matrix?
Matrix Scalar Multiple
Elementary Row Operations
Finding inverse using RREF (Gauss-Jordan)
Finding Matrix Rank using RREF
Is Singular Matrix?
Matrix Generalized Inverse
Solving System of Linear Equations
Linear combination, Span & Basis Vector
Linearly Dependent & Linearly Independent
Change of basis
Matrix Nullity & Null Space
Matrix Eigen Value & Eigen Vector
Matrix Eigen Value & Eigen Vector for Symmetric Matrix
Similarity Transformation and Matrix Diagonalization
Singular Value Decomposition
Resources on Linear Algebra
Reduced Row Echelon Form (RREF)
There is a standard form of a row equivalent matrix that if we do a sequence of row elementary operations to reach this standard form, we may gain the solution of the linear system. The standard form is called Reduced Row Echelon Form of a matrix, or matrix RREF in short.
An m by n matrix is called to be in reduced row echelon form when it satisfies the following conditions:
When only the first three conditions are satisfied, the matrix is called in Row Echelon Form (REF).
You will find that the educational program below is awesome. The interactive program gives many examples to compute the Reduced Row Echelon Form of a matrix input using the three row elementary operations. The computation will show you step by step through both REF and RREF.
How to use?
Simply click Random Example button to create new random input matrix, then click “Matrix RREF” button to get the whole sequence of elementary row operations from the input matrix up to the RREF. The results can be in either rational or decimal format.
Yes, this program is a free educational program!! Please don't forget to tell your friends and teacher about this awesome program!
Preferable reference for this tutorial is
Teknomo, Kardi (2011) Linear Algebra tutorial. http:\\people.revoledu.com\kardi\ tutorial\LinearAlgebra\