How do you solve using gaussian elimination or gauss-jordan elimination, #3w-x=2y + z -4#, #9x-y + z =10#, #4w+3y-z=7#, #12x + 17=2y-z+6#?
Gaussian elimination involves the gradual elimination of variables from the set of equations until values can be found for each variable.
First reorder the terms in all equations so that they all have the same order of variables.
Adding the first two equations together gives
Adding the second pair of equations gives
Adding the middle pair of equations gives
In a similar process, add three times the middle equation to the first equation
Take twice the middle equation from the third equation
Now add four times the first equation to fifteen times the second equation
Substitute this back into one of the final pair of equations to get