Question

The following system of equations has a unique solution.


x−5y−9z=−21


−2x+5y−2z=−33


3x−4y+5z=42


You will solve this system using the method of Gauss-Jordan elimination.


Note, you CANNOT interchange rows of the matrix at any step.


Please follow exactly the instructions provided

Answer 1

Here is the matrix of the given system:

& 1 -5 -9 | -21
-2& 5 -2 | -33
& 3 -4& 5 |& 42

Let's perform Gauss-Jordan elimination:


& 1 -5 -9& | -21
& 0 -5 -20 | -75
& 0& 11 32 |& 105

& 1 -5 -9& | -21
& 0 -5 -20 | -75
& 0& 0 -12 |& 60

& 1 -5 -9& | -21
& 0 -5 -20 | -75
& 0& 0 -1& | -5

& 1 -5& 0& |& 24
& 0 -5& 0& |& 25
& 0& 0 -1& | -5

& 1 -5& 0& |& 24
& 0 -1& 0& |& 5
& 0& 0& 1& |& 5

& 1& 0& 0& | -1
& 0 -1& 0& |& 5
& 0& 0& 1& |& 5

& 1& 0& 0& | -1
& 0& 1& 0& | -5
& 0& 0& 1& |& 5

So, solution is (-1,-5,5).