### Elementary Row Operations

• (Interchange) Interchange two equations
• (Scaling) Multiply an equation by a non-zero constant
• (Replacement) Replace one row by the sum of itself and a multiple of another row [like r2'= -3r1 + r2]

### Systematic Method to achieve Gaussian Elimination

• Save the x term in equation 1 and use it to eliminate all the other x terms below it via rk' = c r1 + rk
• Ignore equation 1 and use the y term in equation 2 to eliminate all the y terms below it.
• Continue until the matrix is in Gaussian or echelon form, with 0s below the diagonal (interchange rows as needed)
• If the system is consistent then the last row with non-zero coeffients will yield xk=b, and then back substitution can be used to solve for the variables.

### Continuing to Gauss-Jordan/ReducedRowEchelon form

• Scale the last row with non-zero coefficients so that the diagonal entry is a 1.
• Use the last non-zero equation to eliminate the spots above it
• Repeate these steps using the second last non-zero equation.
• Continue until the matrix is in Gauss-Jordan/ReducedRowEchelon form with 0s or 1s on the diagonal and 0 coeffients everywhere else.