Using Gauss-Jordan Elimination to find the Inverse of a 3 x 3 Matrix

[@remitto8367]

This was super helpful. Thanks so much

[@molloymaths1092]

No problem. Glad it helped.

[@civilengineer1919]

Good.

[@williamgichuhi6698]

Very educative🇰🇪🇰🇪

[@molloymaths1092]

Thanks

[@rb4ever15]

Every step is intuitive for me.. except for the very first one, which is just changing the order of rows. Obviously, this does not change the nature of the system of linear equations, but don't you end up making operations on rows which you would usually make on another row? Maybe I'm missing something very simple, but isn't that like saying, for example, when you have matrix A= 1 2 4 3 5 0 7 1 1 and matrix B= 1 2 4 7 1 1 3 5 0 that A=B ? I mean, you are performing the same operations on the right-hand side. However, had you not changed the order of rows, the operations would have been done on another row, meaning that eventually the inverse should look the same, except that the rows are swapped. The confusing part for me, however, is that I let an online calculator compute the inverse of the herein given matrix, and it verifies your solution. Conversely, this implies that you should get the same solution, regardless whether you change the order of rows along the process or not. It is just not straightforward for me to grasp.

[@molloymaths1092]

The reason I changed rows 2 and 3 was to get a 1 in the middle row and column. There may be many other ways to approach this problem. This is just one way.

[@rb4ever15]

@@molloymaths1092 don't get me wrong, I understand that. It just does not make intuitive sense to me that such a swap of rows is allowed and eventually yields the same solution. That was my point.

[@molloymaths1092]

@@uw3731 The way I started it, swapping the rows of the matrix also swaps the rows of the Identity matrix in the first step. However It doesn't matter what order you start the rows of the matrix in before this step as you will get the same answer but with different operations since you are also starting with the identity matrix with the rows NOT swapped.

[@brandontinashe3037]

Sorry to ask isn't it Gauss Jordan elimination method??? Not Gaussian elimination method

[@molloymaths1092]

Yes it is. When using RREF it's Gauss Jordan Elimination. When using REF it's Gaussian Elimination. I have used RREF in this video. I think I mention Gauss Jordan at the end of the video. Thanks for the comment.

[@prayashthapa3982]

Doesn't work... For me at least. But this does => r3-r1 r1+r2 r2x-1 r2+2r3 r1-2r3

[@molloymaths1092]

Had another look at my calculations. It seems fine to me. Couldn't get your method to work I'm afraid.

[@user-mx1hm7ju8q]

Just keep on doing doesnt matter,you get the answer anyway.

[@1.6msubscribers8]

kzbin.info/aero/PLCz0Ss_uiYRpf-kwFLByJXHHyCCGyTYa6 Watch it once... lots of calculator tricks

[@AbyssAssassin]

It is gauss gauss Jordan method not elimination 😶

[@molloymaths1092]

See below!!