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Linear Algebra
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# Problem set - Introduction to Vectors (Linear Algebra)

schedule Dec 30, 2023
Last updated
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Linear Algebra
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Compute the following:

$$2 \begin{pmatrix} 3\\1 \end{pmatrix}$$
Show solution

Multiply each component by the scalar constant like so:

$$2\begin{pmatrix} 3\\1 \end{pmatrix}= \begin{pmatrix} 2\times3\\2\times1 \end{pmatrix}= \begin{pmatrix} 6\\2 \end{pmatrix}$$

Compute the following:

$$\begin{pmatrix} 2\\3 \end{pmatrix}+ \begin{pmatrix} 1\\-1 \end{pmatrix}$$
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$$\begin{pmatrix} 2\\3 \end{pmatrix}+ \begin{pmatrix} 1\\-1 \end{pmatrix}= \begin{pmatrix} 3\\2 \end{pmatrix}$$

Compute the following:

$$\begin{pmatrix} 1\\4 \end{pmatrix}- \begin{pmatrix} 1\\-1 \end{pmatrix}$$
Show solution

To subtract two vectors, perform the subtraction for each pair of components like so:

$$\begin{pmatrix} 1\\4 \end{pmatrix}- \begin{pmatrix} 1\\-1 \end{pmatrix}= \begin{pmatrix} 0\\5 \end{pmatrix}$$
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