Blog #10: Gaussian with back substitution vs gaus Jordan

We can also solve systems of linear equations with matrices. The key to solving any system with matrices is forming an augmented matrix, which we can find by using the coefficients of the variables. Remember that the columns are the variables and the rows are the values of the coefficients for each equation. From there we can solve using the Gaussian elimination method or the Gaus Jordan method.

Elementary Row Operations

1. We can interchange 2 rows

2. Multiply a row by a constant

3. Add two rows together.

Steps to Gaussian elimination

1. Create an augmented matrix

2. Use ERO's to rewrite in row echelon form

3. Write a system of equations and use back substitution.

Make sure that everything below your leading ones are zero. The top values don't have to be zero.

Be sure to work column by column.

Steps to Gaus Jordan Method: essentially we are using the same steps as the other elimination method. however, it is important to note that we should only have leading ones and zeroes. Therefore we don't need any new systems of equations. 

Sample problem #1 is  using the Gaus Jordan method. Sample problem #2 is solved using Gaussian elimination. 

Remember that whenever we multiply an equation by a constant, we have to multiply everything in that row. This is shown through the error of another student.