Vectors, mappings, and matrices

Compute the magnitude of

1. $\begin{bmatrix} 1 \\ 3 \end{bmatrix}$
2. $\begin{bmatrix} 2 \\ 3 \\ -1 \end{bmatrix}$
3. $(-2,1,-2)$

Find the unit vector in the direction of the given vector

1. $\begin{bmatrix} -1 \\ 1 \end{bmatrix}$
2. $\begin{bmatrix} 1 \\ -1 \\ 2 \end{bmatrix}$
3. $(2,-5,2)$

Compute

1. $\begin{bmatrix} 3 \\ 1 \end{bmatrix} + \begin{bmatrix} 6 \\ -3 \end{bmatrix}$
2. $\begin{bmatrix} -1 \\ 2 \end{bmatrix} - \begin{bmatrix} 2 \\ -1 \end{bmatrix}$
3. $-\begin{bmatrix} -5 \\ 3 \end{bmatrix}$
4. $2\begin{bmatrix} -2 \\ 4 \end{bmatrix}$
5. $3\begin{bmatrix} 1 \\ 0 \end{bmatrix} + 7 \begin{bmatrix} 0 \\ 1 \end{bmatrix}$
6. $2\begin{bmatrix} 2 \\ -3 \end{bmatrix} - 6 \begin{bmatrix} 2 \\ -1 \end{bmatrix}$

If the magnitude of $\vec{x}$ is 5, what is the magnitude of

1. $4\vec{x}$
2. $-2\vec{x}$
3. $-4\vec{x}$

Suppose a linear mapping $F \colon {\mathbb R}^2 \to {\mathbb R}^2$ takes $(1,0)$ to $(1,-1)$ and it takes $(0,1)$ to $(2,0)$. Where does it take

1. $(1,1)$
2. $(0,2)$
3. $(1,-1)$