Math 260, Fall 2015, Assignment 3

No doubt many people feel that the inclusion of mathematics among the arts is unwarranted. The strongest objection is that mathematics has no emotional import. Of course this argument discounts the feelings of dislike and revulsion that mathematics induces....

- Morris Kline, Mathematics in Western Culture

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

1. Coefficient matrix (of a system of linear equations).
2. Transformation (from $\mathbb{R}^m$ to $\mathbb{R}^n$).
3. Linear transformation (from $\mathbb{R}^m$ to $\mathbb{R}^n$).

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

1. Theorem concerning representability of linear transformations by matrices (also please know the general procedure to compute representing matrices).
2. Theorem concerning linearity of transformations defined by matrices.

Solve the following problems:

1. Section 2.1, problems 1, 2, 3, 4, 5, and 6.
2. Section 2.2, problems 1 and 2.

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