Math 260, Spring 2017, Assignment 13

"Reeling and Writhing, of course, to begin with," the Mock Turtle replied; "And then the different branches of Arithmetic - Ambition, Distraction, Uglification, and Derision."

- Lewis Carroll, Alice's Adventures in Wonderland

Carefully state the following theorems (you do not need to prove them):

1. Four fundamental properties of the determinant.
2. Effect of elementary row operations on the determinant.
3. Theorem relating determinants to invertibility.
4. Cramer's Rule.
5. Theorem concerning the determinant of a product.
6. Theorem concerning the determinant of the transpose.
7. Theorem concerning the determinant of an orthogonal matrix.
8. Theorem relating determinants to hypervolumes of hyperparallelepipeds.
9. Theorem relating $\mathrm{det}(A)$ to the "magnification factor" of the linear transformation determined by $A$.

Solve the following problems:

1. Section 6.1, problems 31, 33, and 39.
2. Section 6.2, problems 1, 5, 9, 11, 15, 37, 38, 39, and 40.
3. Section 6.3, problems 1, 2, 3, 13, 23, and 27.

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