Introduction to Column Vectors Flashcards

All 5 cards in this deck

What does the column vector $\begin{pmatrix}x\\y\end{pmatrix}$ describe?

e.g. $\begin{pmatrix}5\\-2\end{pmatrix}$

Top number = movement right (negative = left), bottom number = movement up (negative = down).

e.g. 5 right and 2 down.

What are the steps to add or subtract two column vectors?

e.g. $\begin{pmatrix}3\\4\end{pmatrix}+\begin{pmatrix}5\\-2\end{pmatrix}$

1. Combine the top numbers: $3+5=8$
2. Combine the bottom numbers: $4+(-2)=2$
3. Write as one column vector: $\begin{pmatrix}8\\2\end{pmatrix}$

How do you multiply a column vector by a scalar?

e.g. $3\begin{pmatrix}2\\-1\end{pmatrix}$

Multiply each component by the scalar.

e.g. $\begin{pmatrix}6\\-3\end{pmatrix}$

True or false? $-\mathbf{a}$ has the same length as $\mathbf{a}$ but points in the opposite direction.

True. Negating a vector reverses its direction and leaves its length unchanged.

How is a vector written in print, and how should you write it by hand?

Print: bold lower case, $\mathbf{a}$. By hand: underlined, $\underline{a}$.