Math 260, Fall 2017, Assignment 12

"When I think of Euclid even now, I have to wipe my sweaty brow."

- C. M. Bellman

Read:

1. Section 6.1.

Carefully define the following terms, then give one example and one non-example of each:

1. Inversion (in a pattern $P$).
2. Sign (of a pattern $P$).
3. Product (of a pattern $P$).
4. Determinant (of a matrix $A$).

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

1. Formula for the number of patterns in an $n\times n$ matrix.
2. Sarrus' rule (for the determinant of a $3\times3$ matrix).

Solve the following problems:

1. Section 6.1, problems 5, 7, 9, 13, 43, 44, and 48.

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