Math 260, Fall 2019, Assignment 14

Algebra begins with the unknown and ends with the unknowable.

- Anonymous

Read:

1. Section 6.3.

Carefully describe the following algorithms:

1. Procedure to compute $\mathrm{det}(A)$ by row-reduction.

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

1. Theorem relating determinants to invertibility.
2. Theorem on Laplace expansion (Theorem 6.2.10 in the text).
3. Theorem concerning the determinant of a product.
4. Theorem relating a $2\times2$ determinant to the area of a parallelogram.

Solve the following problems:

1. Section 6.2, problems 29, and 45 (Hint for both: use Laplace expansion.)
2. Section 6.3, problems 1, 2, and 3 (Hint for 2 and 3: a triangle is half of a parallelogram.)

--------------------End of assignment--------------------