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)

(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.