Math 260, Spring 2017, Assignment 7

Mathematicians are like Frenchmen: whatever you say to them they translate into their own language, and forthwith it is something entirely different.

- Goethe

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

1. Domain (of a linear transformation $T:\mathbb{R}^m\rightarrow\mathbb{R}^n$).
2. Codomain (of a linear transformation).
3. Image (of a linear transformation).
4. Kernel (of a linear transformation).

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

1. Properties of the image (this is Theorem 3.1.4 in the text).
2. Properties of the kernel (Theorem 3.1.6).
3. Characterizations of invertible matrices (Summary 3.1.8).

Solve the following problems:

1. Section 3.1, problems 1, 3, 5, 7, 12, 14, 15, 17, 19, 23, and 25.

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