RREF, or reduced row echelon form, is a method of simplifying a system of linear equations. To get rref with a variable in the last column, you can use the Gauss-Jordan elimination method, which involves performing a series of row operations on the augmented matrix until it is in rref. This will result in the variable being isolated in the last column.
Using rref with a variable in the last column can help you to easily solve a system of linear equations and find the values of the variables. It also allows you to identify if the system is consistent or inconsistent, and if consistent, how many solutions it has.
The process of obtaining rref with a variable in the last column involves converting the system of linear equations into an augmented matrix, performing row operations to simplify the matrix, and then converting it back into equations. This will result in the variable being isolated in the last column in its simplest form.
While using rref with a variable in the last column can be a useful method for solving linear equations, it may not always be the most practical or efficient method. In some cases, it may be easier to use substitution or elimination to solve the system of equations.
To check if your rref with a variable in the last column is correct, you can substitute the values of the variables obtained back into the original equations and see if they satisfy the equations. You can also use software or online calculators that can perform rref calculations and verify your results.