Math 260, Fall 2015, Assignment 6

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

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

1. Subspace (of $\mathbb{R}^n$).
2. One-to-one function.
3. Onto function.
4. Kernel (of a linear transformation).

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

1. Theorem relating spans to subspaces.
2. Theorem relating images to subspaces.
3. Theorem relating kernels to subspaces.
4. Theorem relating kernels to one-to-oneness.

Solve the following problems:

1. Section 3.1, problems 23, 25, 27, 32, and 33.
2. Section 3.2, problems 1, 2, 3, 6, and 7.

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