1. Among other operations are computations of matrix inverses and lower echelon forms . 2. T and reduce it to row echelon form : 3. The reduced row echelon form of a matrix may be computed by Gauss Jordan elimination. 4. Elementary row operations are used in Gaussian elimination to reduce a matrix to row echelon form . 5. They are also used in Gauss-Jordan elimination to further reduce the matrix to reduced row echelon form . 6. With modern computers, Gaussian elimination is not always the fastest algorithm to compute the row echelon form of matrix. 7. On the other hand, the reduced echelon form of a matrix with integer coefficients generally contains non-integer coefficients. 8. The number of independent equations in the original system is the number of non-zero rows in the echelon form . 9. If the matrix is further simplified to reduced row echelon form , then the resulting basis is uniquely determined by the row space. 10. Using row operations to convert a matrix into reduced row echelon form is sometimes called "'Gauss Jordan elimination " '.
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