Many thanks for having such a beautifully cleaned blackboard and such clearly written symbols. When looking at the lectures from a small screen this makes a great difference, especially when tensorial notations is involved where primed subscripts are often used.
Nice video though I have a question. It could have well been bc - ad = 0, which is definitely not how we see determinants. Any reason why its the other way round?
Useful video to better explain what was taught rather superficially to me in A-level further maths. Just one question: From ad=bc, it is immediate that ad-bc=0 or alternatively bc-ad=0 or alternativley |ad-bc|=0. Why is the first of these options, ad-bc, chosen to be the determinant, rather than either of the other two?
It's ad-bc so that the determinant of the identity matrix is 1 and not 1. It's not the absolute value because we want the determinant to change sign when columns are switched.
In case it isn't obvious, he meant that "we want the determinant of the identity matrix to equal 1 and not -1". He just forgot the negative sign in front of the second 1 in the sentence.
Yes, because the columns are linearly dependent. Anytime they are independent you get a non-zero value. In 2D that will be the area of parallelogram, in 3D the volume of a parallelepiped, and in higher dimensions ... well, you get the point.
