Math 260, Fall 2018, Assignment 2

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

Read:

1. Section 1.2.
2. Section 1.3.

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

1. Augmented matrix (of a system of linear equations).
2. Elementary row operation.
3. Row-equivalent (matrices).
4. Reduced row-echelon matrix.
5. Pivot (of a reduced row-echelon matrix).
6. Rank (of a matrix; note that we did not discuss this in class, so you will need to look in the book for the definition).
7. Reduced row-echelon form (of a given matrix $A$; also known as $\mathrm{rref}(A)$).

Carefully describe the following algorithms:

1. Gauss-Jordan elimination algorithm.

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

1. Theorem relating the solution-sets of linear systems represented by row-equivalent matrices.
2. Theorem concerning the number of reduced row-echelon matrices to which a given matrix is row-equivalent.

Solve the following problems:

1. Section 1.2, problems 1, 5, 7, 9, 11, 18, 19, 21, and 22.
2. Section 1.3, problems 1, 2, and 3.

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