# Become a Linear Algebra Expert

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Lesson /10
Vector Arithmetic

Vectors, just like real numbers can be added and subtracted.\\
$$\vec{x} = \begin{bmatrix}x_1\\x_2\\.\\.\\.\\x_n\end{bmatrix}, \vec{y} = \begin{bmatrix}y_1\\y_2\\.\\.\\.\\y_n\end{bmatrix}$$.

Then,

$$\vec{x}+\vec{y} = \begin{bmatrix}x_1+y_1\\x_2+y_2\\.\\.\\.\\x_n+y_n\end{bmatrix}$$

and

$$\vec{x}-\vec{y} = \begin{bmatrix}x_1-y_1\\x_2-y_2\\.\\.\\.\\x_n-y_n\end{bmatrix}$$

Also, you can multiply a scalar value to a vector.

$$t\vec{x} = \begin{bmatrix}tx_1\\tx_2\\.\\.\\.\\tx_n\end{bmatrix}$$
$t \in \mathbb{R}$

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