Math 260, Fall 2017, Assignment 5

I tell them that if they will occupy themselves with the study of mathematics, they will find in it the best remedy against the lusts of the flesh.

- Thomas Mann, The Magic Mountain

Read:

1. Section 2.4.

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

1. Composition (of two transformations).
2. Inverse (of a transformation).

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

1. Theorem relating composition of linear transformations to matrix multiplication.
2. Formula for the inverse of a $2\times2$ matrix.

Carefully describe the following algorithms:

1. Algorithm to determine whether a matrix has an inverse, and to compute the inverse if it does.

Solve the following problems:

1. Section 2.4, problems 1, 3, 5, 7, 9, 11, 13, 17, 19, and 41.

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