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# Answer on Matrix | Tensor Analysis Question for vinita

Question #6404
The following system of equations has a unique solution.

x&minus;5y&minus;9z=&minus;21

&minus;2x+5y&minus;2z=&minus;33

3x&minus;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.

Here is the matrix of the given system:

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

Let&#039;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).

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