"So there is definitely work hiding there" Thank you so much, Jim, for your love for math and ability to walk students through! Over the years you've helped me so much to refresh the college algebra and understand it much better with your videos and courses!
So glad your back at it. Your enthusiasm is absolutely infectious. Just wish I could get my teenage sons to watch 1 or 2 of your videos. I think they would be hooked.
Thank you for making such videos. I nearly lost hope while thinking about this identity. Even though I like the subject, this self study thing is taking a toll on me as I am learning everything on my own. I feel lucky for being born in this modern era, as I can get some insights from professors like you. Thank you once again.
I know this was made about 7 years ago, but I still want to provide a quick proof by contradiction for why if A is not invertible, then AB is not invertible: Let AB be invertible. Then, there exists such a matrix C that when multiplied with AB yields the identity matrix, I. We can write this as an equation: AB * C = I Now through associative property of matrices, we find A * BC = I So if AB is invertible, A must be invertible as well. Therefore when A is not invertible, AB must be not invertible as well.
This is useful - but all the facts it relies on are totally left in the air - I think I'm there already, but I think there should be an elaboration, development, of each of the parts you're using, because unless brings those pieces, this video, by itself is useless. And, I'm betting, you could explain each of them - maybe make a play list with this video as the capstone / contents and each little equation you wrote down getting a video of it's own.
