Miss V's daughter, Kara, followed in her footsteps and taught the ways of Matrices and Systems of equations. The two ways to solve system of equations with matrices, Gaussian Elimination and Gauss-Jordan Elimination. To use these techniques, one must know Elementary Row Operations, the ways of which one can manipulate matrices to get numbers where they want. These operations include: 1) interchange any two rows 2) multiply a row by a non-zero constant 3) add one row to another.
The Gaussian Elimination with Back-Substitution method steps are as follows:
-Write the augmented matrix of the system of linear equations
-Use elementary row operations to rewrite the augmented matrix in row-echelon form
-Write the system of linear equations corresponding to the matrix in row-echelon form, and use back-substitution to find the solution
Make sure that you have a leading 1 and that the main diagonal is consisted of 1's. Everything under the main diagonal has to be zeros but above the main diagonal there can be any numbers.
The Gauss-Jordan Elimination method steps are as follows:
-Write the augmented matrix of the system of linear equations
-Use elementary row operations to rewrite the augmented matrix in row-echelon form
-Write the system of linear equations corresponding to the matrix in row-echelon form
Make sure that you have a leading 1 and that the main diagonal is consisted of 1's. Everything under and above has to be zeros.
I personally like to use the Gauss-Jordan elimination. It is better and simpler. It saves more time. Thanks for putting both ways up there. It is important to know the differences in both ways. Thanks again!
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