Math 260, Fall 2018, 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 2.3.

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

1. $\mathrm{Proj}_{\vec v}(\vec x)$.
2. Composition (of two functions $f:\mathbb{R}^n\rightarrow\mathbb{R}^p$ and $g:\mathbb{R}^m\rightarrow\mathbb{R}^n$).
3. Inverse (of a function $f:\mathbb{R}^m\rightarrow\mathbb{R}^n$).

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

1. Theorem concerning parallel and perpendicular components.
2. Formula for the matrix representing a rotation in $\mathbb{R}^2$.
3. Theorem concerning linearity of the composition of two linear transformations.
4. Formula for the matrix representing the composition of two linear transformations.

Solve the following problems:

1. Section 2.2, problems 6, and 10.
2. Section 2.3, problems 33, 35, 39, 43, 45, and 46.

--------------------End of assignment--------------------