Linear Algebra 14TBD: Determinant-Based Derivation of the Triangle Area Formula

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havent we proofed in the previous video that the determinant is signed area/volume than we input in it the basis vectors (which by definition are 1, 0, 0 ; 0, 1, 0 ; 0, 0, 1) only? when we decompose the vectors a, b here, we get the "complex" matrix. we can not use one of the properties checked, on which we built the proof : | Identity | =1 anymore, no? We have some work to do (GE) to reach the Identity matrix here, but then we will proof again - the trivial area = 1 [some unit squared] of the BASIS UBIT CELL - not the area of the vectors I AM missing something - as always

atnn

Are e1 and e2 unit vectors? I'm not sure how e2*b*sin(gamma) would give you the y coordinate of the vector b unless e2 = 1. It looks like it doesn't matter what angle e2 is, am I missing something? P.S. great videos, they're some of the best on YouTube.

arcanernz

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