By far, the best online course on linear algebra out there. It offers an unparalleled level of depth and simplicity to the subject. Thank you very much.
The usefulness of your videos wasn't obvious for me at first. Now I've watched all of them and linear algebra's become one of my favorite areas in high school mathematics :) You should also invite people that are watching your videos to watch 3blue1brown's videos about linear algebra, they're very helpful in visualizing how matrices work and how determinant is affected by modifications of the matrix. It really makes fundamental properties of the determinant very very easy to understand! Thank you :)
I gasped when this proof hit me. Beautiful stuff. This is a feeling only math (and problems that fundamentally boil down to math) gives me. Thank you for the great explanation.
here we do everything w.r.t columns, but going with this approach, we do not have that |At|=|A| yet....so we really should do w.r.t to rows, no? Tat this point, the alternating property is for rows, so switching ( 1 1 ) with ( 0 0 ) in the first zero determinant does not so clearly leads to zero, no?
Sir I have a question, If the determinant you began with had an entry of 0 in say, the first column, then wouldn't that result in the determinant being subdivided into n-1 determinants as opposed to n determinants? If you insist on subdividing into n determinants then wouldn't that imply that one of those determinants has a column of all 0s?
@@MathTheBeautiful Never mind. The importance of your lecture for me was not the new way of defining the determinant, but rather the technique outlined in 0:48 Thank you!
Excuse my ignorance, but for the notation with the dots on the sides of vectors ( .a., but the periods are raised slightly), does this just denote that it is a row vector? Thanks in advance.
