Math 260, Fall 2017, Assignment 1

By one of those caprices of the mind, which we are perhaps most subject to in early youth, I at once gave up my former occupations; set down natural history and all its progeny as a deformed and abortive creation; and entertained the greatest disdain for a would-be science, which could never even step within the threshold of real knowledge. In this mood of mind I betook myself to the mathematics, and the branches of study appertaining to that science, as being built upon secure foundations, and so, worthy of my consideration.

- Mary Shelley, Frankenstein

Read:

1. Sections 1.1 and 1.2.

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

1. Linear system (a.k.a. "system of linear equations").
2. Augmented matrix (of a linear system).
3. Coefficient matrix (of a linear system).
4. Augmentation vector (of a linear system).
5. Elementary row operation.
6. Row-equivalent matrices.

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

1. Statement relating the solution sets of row-equivalent matrices.

Carefully describe the following algorithms:

1. Gauss-Jordan elimination.

Solve the following problems:

1. Section 1.1, problems 1, 3, 4, 11, 15, 24, and 30. (You are not required to use the "official" Gauss-Jordan algorithm in this section, but it's not a bad idea to try.)
2. Section 1.2, problems 1, 2, 4, 5, and 7. (In these problems, simply run the Gauss-Jordan algorthm on the augmented matrix. In some cases you will see how to read off the solutions of the system from the output of the algorithm, and in other cases you might not. We will discuss this issue on Tuesday.)

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