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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 |
Finding inverse using RREF (Gauss-Jordan) We can use the three elementary row operations to find the row equivalent of Reduced Row Echelon Form (RREF) of the matrix input. In this page you will learn that using the same technique, you can obtain matrix inverse. This technique is called Gauss-Jordan method. Gauss Jordan method is based on the following theorem: The method to find inverse using Gauss Jordan method is as follow: To give you example on how to compute step by step Gauss Jordan methhod, I make a matrix calculator below. The interactive calculator below can give you as many examples as you wish to compute matrix inverse using Gauss Jordan method systematically. Yes, this program is a free educational program!! If you like it, please recommend this fascinating program to your friends. The program shows you step by step of the three row elementary operations to reach the Reduced Row Echelon Form of the matrix input. How to use? Simply click Random Example button to create new random input matrix, then click “Matrix Inverse using Gauss Jordan” button to get the whole sequence of elementary row operations from the input matrix up to the RREF and matrix inverse. The results can be in either rational or decimal format.
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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