Math 260, Spring 2017, Assignment 2

The beginner...should not be discouraged if...he finds that he does not have the prerequisites for reading the prerequisites.

- P. Halmos

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

1. Reduced row echelon form.
2. Pivot (of a reduced row echelon matrix).
3. Pivot variable (of a system of linear equations, in reduced row echelon form).
4. Row-equivalent (matrices).
5. $\mathrm{rref}(A)$.
6. Row-reduction algorithm.
7. Geometric vector.

Carefully describe the following procedures:

1. Gauss-Jordan elimination.
2. Procedure to determine the solutions of a linear system from its reduced row-echelon form.

Solve the following problems:

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

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