Comments by "" (@retagainez) on "The determinant | Chapter 6, Essence of linear algebra" video.

  1. my professor taught us a neat shortcut for dets for 3x3 matrix( and i guess any other square matrix), you take the first two columns and make a copy of the matrix with those same two columns added to the end of your new matrix, let me try to illustrate this in this comment 1 4 7 1 4 7 1 4 2 5 8 --> 2 5 8 2 5 3 6 9 3 6 9 3 6 so as i described earlier, you take the 3x3 matrix, and basically make it into a 3x5 matrix, this is just to compute the determinant and doesn't have any other purpose other than that as far as i see. so to compute the determinant using this new matrix you multiply all the diagonals going from top left to bottom right so starting from the left most one, ( 1*5*9 + 4*8*3 + 7*2*6 ) this is half of the determinant now we need to do it going backwards, from top right to bottom left, ( 4*2*9 + 1*8*6 + 7*5*3 ), this is the second half of computing the determinant now we combine both of these sums, but the second half subtracts from the first half so: ( 1*5*9 + 4*8*3 + 7*2*6 ) - ( 4*2*9 + 1*8*6 + 7*5*3 ) = det of the matrix, hope I remembered this correctly!
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