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Matrix Size & Validation
Vector Algebra What is Vector? Vector Norm Unit Vector Vector Addition Vector Subtraction Vector Scalar Multiple Vector Multiplication 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 Matrix Algebra What is a matrix? Special Matrices Matrix One Null Matrix Matrix Diagonal Is Diagonal Matrix? Identity Matrix Matrix Determinant Matrix Sum Matrix Trace Matrix Basic Operation Is Equal Matrix? Matrix Transpose Matrix Addition Matrix Subtraction Matrix Multiplication Matrix Scalar Multiple Hadamard Product Horizontal Concatenation Vertical Concatenation Elementary Row Operations Matrix RREF Finding inverse using RREF (Gauss-Jordan) Finding Matrix Rank using RREF Matrix Inverse Is Singular Matrix? Linear Transformation Matrix Generalized Inverse Solving System of Linear Equations Linear combination, Span & Basis Vector Linearly Dependent & Linearly Independent Change of basis Matrix Rank Matrix Range Matrix Nullity & Null Space Eigen System Matrix Eigen Value & Eigen Vector Symmetric Matrix Matrix Eigen Value & Eigen Vector for Symmetric Matrix Similarity Transformation and Matrix Diagonalization Matrix Power Orthogonal Matrix Spectral Decomposition 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). Using Reduced Row Echelon Form of a matrix we can calculate matrix inverse, rank of matrix, and solve simultaneous linear equations. 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! See also: elementary row operations, matrix inverse using Gauss Jordan, rank of matrix through RREF, and solving simultaneous linear equations. Rate this tutorial or give your comments about this tutorial Preferable reference for this tutorial is Teknomo, Kardi (2011) Linear Algebra tutorial. http:\\people.revoledu.com\kardi\ tutorial\LinearAlgebra\ |
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