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If Det(A) is the change in volume, I would expect the sign to indicate whether the volume increased or decreased rather than the orientation. Can I get some more insight on why it doesn't tell me the increase/decrease of volume?


Can a given linear map only mirror once? If you mirror horizontally and then vertically, is this equivalent to no mirroring? The fact that the determinant can only either be positive or negative would suggest this.


How does it measure the change in volume? Could we go over it more in class?


What happens if the determinant is zero? (can there be a case?)


Does this mean the change in volume from a cube with dimensions (1,1,1)?


How would this apply to structures that are difficult to represent with matrices?


Can we think of the matrix as implementation and determinant as an abstract concept?


if the direction changes along two dimensions, will the result still be positive?


Why do we care about the change in volume and could we do a mathematical example about how the determinant tells the change in volume?


Not exactly familiar with how determinant describes a change in volume. How would we take the determinant in the above two cases to show that? Could we get examples?


Do determinants represent anything for higher dimension matrices?