Determinant of a Triangular Matrix

[@patrickjmt]

Any tips or tricks you would like to share to help find determinants? I'd love to hear and I bet others would too :)

[@Midnight_Star1021]

Thank you for the video! I dont understand how most of this works (I should probably watch your other videos), but video was great 👍👍

[@lukieg420]

What is the point of the determinant? I always liked doing matrix problems bc it’s like a little puzzle but what is like the Mathematical significance of this number

[@darksteel78]

3blue1brown has an interesting series on matrices and linear algebra. It's very conceptual but shows an interesting way of thinking about matrices and linear algebra. One of them is about the determinant of a matrix and what it means: kzbin.info/www/bejne/f6GWiWyChM1lms0. TL;DW: The geometric interpretation is that the determinant tells the scaling factor of the transformation represented by the matrix. A 2x2 matrix with a determinant of 2 would transform an input shape such that its area is double the original shape. A negative determinant would flip the orientation of the shape. This can also be seen in the inverse of a matrix. The determinant of the inverse is the reciprocal of the determinant of the original: det(A^-1) = 1/det(A). If you think of this as restoring the transformed shape back into the original shape, the inverse transformation must scale the new shape by multiplying by the reciprocal of the scaling factor from the original transformation. One interesting property of this is that the determinant can be used to check whether a matrix is invertible. If the determinant of a 2x2 matrix is 0, you can imagine it transforming an input shape down into a single point because the area becomes 0. You can't get back to the original shape from 1 point. You can't reverse the squashing because the area became 0. Since 0 multipled by any number is 0, the transformation cannot be reversed. In other words, the matrix that represents the transformation cannot be inverted.

[@patrickjmt]

There is actually a good discussion on Reddit ‘why are determinants so useful’ was the question. Lots of good replies!

[@basouta9142]

Good job ❤🎉

[@patrickjmt]

thanks!

[@WinArmendalGaming]

what about those rules that changing sign of matrices? some tutorial told me to change sign, still kinda confusing. anyway, thanks in advance!

[@patrickjmt]

You might be thinking of cofactors!

[@Midnight_Star1021]

Thank you for the video! I dont understand how most of this works (I should probably watch your other videos), but video was great 👍👍

[@Midnight_Star1021]

Thank you for the video! I dont understand how most of this works (I should probably watch your other videos), but video was great 👍👍

[@patrickjmt]

well, this is just a strictly computational video (still super important!) so there is not much light shining on what determinants actually are. if you understand cofactors and minors, you could derive all of this from that stuff :)