[Linear Algebra] Linear Equation

Jason Lee·2022년 8월 4일
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Linear Algebra

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Linear Equation

  • Linear equation in the variables x1,,xnx_1, \cdots, x_n is an equation that can be written in the form like below, where b and the coefficients a1,,ana_1, \cdots, a_n are scalar (real or complex numbers)

a1x1+a2x2++anxn=ba_1 x_1 + a_2 x_2 + \cdots + a_n x_n = b

  • The above equation can be written as below

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

where a=[a1a2an]\textbf{a} = \begin{bmatrix} a_1 \\ a_2 \\ \vdots \\ a_n\end{bmatrix}, x=[x1x2xn]\textbf{x} = \begin{bmatrix} x_1 \\ x_2 \\ \vdots \\ x_n\end{bmatrix}

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