E600 Mathematics

MSc Economics Preparatory Module

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Chapter 1 – Quiz 1

1. Which components are needed to define a vector space?

Set, vector addition and scalar multiplication.

Set, addition and scalar product.

Vector addition and vector product.

Only a set (e.g. $\mathbb R^3$ ).

2. Compute the scalar product $\begin{pmatrix} 2\\4\\0\\3\end{pmatrix} \cdot \begin{pmatrix} -3\\2\\10\\2\end{pmatrix}.$ (Write down only the result as a number; do not use spaces, letters, etc.)

3. Select all vectors that are elements of $\mathbb N^2 \times \mathbb R$ . (Multiple choice)

$\begin{pmatrix}1\\4\end{pmatrix}$

$5$

$\begin{pmatrix}\pi\\1\\2\end{pmatrix}$

$\begin{pmatrix}-1\\3\\0\end{pmatrix}$

$\begin{pmatrix}1\\4\\2\end{pmatrix}$

$\begin{pmatrix}1\\3\\ \pi^2\end{pmatrix}$

4. What ich object is equal to this expression: $\begin{pmatrix}1\\4\end{pmatrix} + 3 \cdot \begin{pmatrix}-2\\5\end{pmatrix}$ ?

$27$

$\begin{pmatrix}-5\\19\end{pmatrix}$

$\begin{pmatrix}7\\-11\end{pmatrix}$

$14$

5. Select all answers where the given vectors are linearly independent. (Multiple choice)

$\begin{pmatrix}1\\4\end{pmatrix}, \begin{pmatrix}0\\1\end{pmatrix}$

$\begin{pmatrix}2\\4\end{pmatrix}, \begin{pmatrix}-1\\-2\end{pmatrix}$

$\begin{pmatrix}1\\2\end{pmatrix}, \begin{pmatrix}2\\3\end{pmatrix}, \begin{pmatrix}-1\\4\end{pmatrix}$

$\begin{pmatrix}1\\3\\4\end{pmatrix}, \begin{pmatrix}4\\-1\\6\end{pmatrix}$

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