Vectors Quiz 3

The following questions need to be answered sequentially in the workspace.

The following is a 2D
vector:

\vec{x}=\begin{bmatrix} a\\b\end{bmatrix}

(a)

What is the magnitude of \alpha\vec{x} ? ( Or in other words, find \left |\alpha\vec{x} \right | ) .

(b)

If \alpha>0 , will the direction of the resulting vector change?

yes / no (case sensitive)

(c)

If \alpha<0 , by how may degrees will the direction of the resulting vector change?

(d)

If -1<\alpha<1 , will \left |\alpha\vec{x} \right | increase or decrease?

(The answer is case sensitive)

Workspace

This section contains either a workspace (it can be a Jupyter Notebook workspace or an online code editor work space, etc.) and it cannot be automatically downloaded to be generated here. Please access the classroom with your account and manually download the workspace to your local machine. Note that for some courses, Udacity upload the workspace files onto https://github.com/udacity , so you may be able to download them there.

Workspace Information:

Default file path:
Workspace type: react-live
Opened files (when workspace is loaded): n/a

(You will find the answer to this quiz at the end of the Vectors lesson)

By knowing how to add vectors and how to multiply them by a scalar , we can define a very important term in Linear Algebra: Linear Combination .

When diving into the world of Artificial Intelligence (or what we refer to as AI), you will see that we frequently need to use linear combinations. But before we jump into simulations of artificial neural networks, let's begin our next lesson, in which Grant will take you through the beautiful graphical aspects of a Linear Combination .

Remember: if you are having issues with the workspace, reset your data.