Module 1: Now You Try II

1. Write a vector in $\mathbb{R}^4$ whose first component is $2$ and each other component is the square of the one above it.

Solution:

$\begin{pmatrix} 2 \\ 4 \\ 16 \\ 256 \end{pmatrix}.$

2. Suppose that the set of scalars you have are only $\{0,1\}$. How many vectors in $\mathbb{R}^2$ can you make?

Solution:

Each vector will have two options for each of its two components. So this gives four total vectors:$\begin{pmatrix} 0 \\ 0 \end{pmatrix}, \begin{pmatrix} 1 \\ 0 \end{pmatrix}, \begin{pmatrix} 0 \\ 1 \end{pmatrix}, \begin{pmatrix} 1 \\ 1 \end{pmatrix}.$