NYC - 2.4 - Inverse of a Partitioned Matrix

[@nathanaelmccooeye3204]

This was my cal 2 teacher. Probably the best teacher I’ve ever had.

[@ВимВом-ф6ы]

Thanks for this video. It is so easy to understanding

[@glenquadros6063]

Thank you for this video. It helped a lot.

[@muqrisalmardi1791]

thank you so much

[@RAinitials]

Thank you so much!!

[@jonjiesarona9237]

Nice

[@FahadKamel-wy3uc]

Hello Doctor, is it possible for you to give us the source of this method? In other words, I want research or a book that uses the method that I mentioned on KZbin.

[@CynthiaMakhosi]

Also looking for it now

[@storycafe.coffee]

Is there a video that explains how (A, C are square matrices) the inverse of matrix M is A-1 - A-1BC-1 0 C-1

[@christophemorris7582]

Hi there! I don't know, but you can find the proof in Linear Algebra and its Applications by David C. Lay. In Section 2.4 of the book (regardless of the edition), about partitioned matrices, that formula is derived. I hope this helps! Christophe

[@storycafe.coffee]

@@christophemorris7582 Thank you so much sir!

[@ryanjackson0x]

How do we know that A is invertible? I know that this can be determined by reducing augmented matrix A|I, but what if the terms of A are not known?

[@christophemorris7582]

Hi! That's a good question. I don't do it in the video, but when we look for the formula for the inverse that's introduced at the beginning, we can prove that A is invertible if and only if A11 and A22 are both invertible. As such, knowing that A11 and A22 are invertible is the only necessary condition for knowing that A is invertible.

[@utkachannel4411]

hi i am newbie in linear algebra, does the task always include that A21 is zero matrix? Or it is the only condition for finding the inverse ?

[@christophemorris7582]

Hi! Yes, you assume that A21 is the zero matrix (so we are considering a "block upper triangular matrix").