Math 260, Fall 2015, Assignment 11

The danger already exists that the mathematicians have made a covenant with the devil to darken the spirit and to confine man in the bonds of Hell.

- Saint Augustine

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

1. $(i,j)$ minor (of a square matrix $A$; often denoted $A_{i,j}$).
2. Determinant (of a $1\times1$ matrix).
3. Determinant (of an $n\times n$ matrix, in terms of $(n-1)\times(n-1)$ determinants).

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

1. Theorem concerning the Gram-Schmidt process.

Solve the following problems:

1. Section 6.1, problems 1, 3, 5, 7, 9, and 11.

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