Then, elementary row operations are used to simplify the matrix.If a matrix is in row-echelon form, that means that reading from left to right, each row will start with at least one more zero term than the row above it.
![]() Some definitions of Gaussian elimination say that the matrix result has to be in reduced row-echelon form. That means that the matrix is in row-echelon form and the only non-zero term in each row is 1. Gaussian elimination that creates a reduced row-echelon matrix result is sometimes called Gauss-Jordan elimination. On one side of the augmented matrix, the coefficients of each term in the linear equation become numbers in the matrix. On the other side of the augmented matrix are the constant terms each linear equation is equal to. The table below shows the row reduction process on the system of equations and on the augmented matrix. Reading this matrix tells us that the solutions for this system of equations occur when x 2, y 3, and z -1. Basically, you eliminate all variables in the last row except for one, all variables except for two in the equation above that one, and so on and so forth to the top equation, which has all the variables. Then you can use back substitution to solve for one variable at a time by plugging the values you know into the equations from the bottom up. Then eliminate the second variable in all equations except for the first two. This process continues, eliminating one more variable per line, until only one variable is left in the last line. You can multiply a row by a constant and then add it to another row to change that row. For example, you can multiply row one by 3 and then add that to row two to create a new row two. ![]() What Is Gaussian Elimination Method How To Get ThisHowever, if you want to know how to get this matrix into reduced row echelon form to find the solutions, follow these steps. ![]()
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