Determinants

Part 5: Summary

Record what you have learned about:

1. The relationship between determinants and invertibility.
2. The relationship between the determinant of an invertible matrix and the determinant of its inverse.
3. The relationship between the determinant of a square matrix and the determinant of its transpose.
4. The relationship between the determinant of a product of matrices and the determinants of the factors.
5. The relationship between the determinant of a sum of matrices and the determinants of the terms.
6. How determinants change (if at all) when each of the three elementary row operations is done to a square matrix.
7. How the determinant changes (if at all) when a square matrix is multiplied by a scalar.
8. Determinants of zero, identity, and triangular matrices.
9. How an inverse matrix can be computed from an adjoint matrix.
10. (optional) What is a Hilbert matrix? How does its determinant suggest it is `close' to being singular?

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