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.
Read off the solutions