Math 260, Fall 2017, Assignment 2

We admit, in geometry, not only infinite magnitudes, that is to say, magnitudes greater than any assignable magnitude, but infinite magnitudes infinitely greater, the one than the other. This astonishes our dimension of brains, which is only about six inches long, five broad, and six in depth, in the largest heads.

- Voltaire

Read:

1. Section 1.3.

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

1. (In) reduced row-echelon form.
2. Reduced row-echelon form (of a given matrix).
3. Pivot (of a matrix in reduced row-echelon form).
4. Dimension (of the solution set of a linear system).
5. Geometric vector.
6. Sum (of two geometric vectors).
7. Scalar multiple (of a geometric vector).
8. Zero vector.

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

1. Statement describing the solutions of a linear system in reduced row-echelon form.

Solve the following problems:

1. Section 1.2, problems 1, 2, 4, 5, and 7 (you have already done Gauss-Jordan elimination on these systems in the previous assignment; now go ahead and write the solutions of these linear systems).
2. Section 1.2, problems 18, 19, 20, 22, and 29.
3. Section 1.3, problems 1, 7, and 8.

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