[Linear Algebra] Linear Equation

Linear Equation

• Linear equation in the variables $x_1, \cdots, x_n$ is an equation that can be written in the form like below, where b and the coefficients $a_1, \cdots, a_n$ are scalar (real or complex numbers)

$a_1 x_1 + a_2 x_2 + \cdots + a_n x_n = b$

• The above equation can be written as below

$\textbf{a}^T \textbf{x} = b$

where $\textbf{a} = \begin{bmatrix} a_1 \\ a_2 \\ \vdots \\ a_n\end{bmatrix}$, $\textbf{x} = \begin{bmatrix} x_1 \\ x_2 \\ \vdots \\ x_n\end{bmatrix}$