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By Kardi Teknomo, PhD.
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Another application of elementary row operations to find the row equivalent of Reduced Row Echelon Form (RREF) of the matrix input is to find matrix rank.
Similar to trace and determinant, rank of a matrix is a scalar number showing the number of linearly independent vectors in a matrix, or the order of the largest square sub-matrix of the input matrix whose determinant is non-zero. Click here to obtain more explanation about matrix rank and the properties of matrix rank.
To compute rank of a matrix through elementary row operations, simply perform the elementary row operations until the matrix reach the Reduced Row Echelon Form (RREF). Then the number of non-zero rows indicates the rank of the input matrix.
The interactive program below finds matrix rank using elementary row operations. It can give you many examples. Simply click “Random Example” button to create new random input matrix. When you click “Matrix Rank” button, the program will show you step by step the sequence of elementary row operations from the input matrix up to the RREF and count the non-zero rows in the matrix RREF as matrix rank.
See also: Matrix RREF, Elementary row operations, matrix rank
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Preferable reference for this tutorial is
Teknomo, Kardi (2011) Linear Algebra tutorial. http:\\people.revoledu.com\kardi\
tutorial\LinearAlgebra\ |
