Cool trick to find any Matrix (Linear Algebra Trick!)

[@MiguelZapateiro]

This is a well-known linear algebra fact, but it's cool that you figured out on your own

[@AbhiramN_1289]

Is there a name for this?

[@MiguelZapateiro]

@@AbhiramN_1289 I'm not entirely sure. It's a pretty direct consequence of linearity.
Since, let's say on R^3, A(1,0,0) is the first column of A, A(0,1,0) is the second and A(0,0,1) is the third. Also, we're talking linear applications, so A(x,y,z) = xA(1,0,0)+yA(0,1,0)+zA(0,0,1).
This means that if you know A(1,0,0), A(0,1,0) and A(0,0,1), no matter what vector v you take, you can always find out Av.
But there's nothing special about (1,0,0), (0,1,0) and (0,0,1), you could choose any other set of three base vectors. In fact the process you show in the video isn't that different from a coordinate change

[@AbhiramN_1289]

@ I guess this makes sense. I have never seen my method taught in class even though it is much simpler.