> [!summary] A matrix is an array of elements >[!info]+ Read Time **⏱ 1 min** # Definition A matrix is an array of elements arranged in rows and columns. A point on the matrix, like $a_{11}$ or $a_{m_{1}}$ is called the **entry**. A common matrix is an array of the coefficients in a system of [[Linear Equations|linear equations]]. There are two types of matrices. The coefficient matrix is an array of the coefficients, excluding the solution value. An augmented matrix is an array of the coefficients and solution values. Any matrix has [[Dimensions of a Matrix|dimensions]]. **Coefficient matrix:** $ A = \begin{pmatrix} a_{11} & a_{12} & \cdots & a_{1n} \\ a_{21} & a_{22} & \cdots & a_{2n} \\ \vdots & \vdots & \ddots & \vdots \\ a_{m1} & a_{m2} & \cdots & a_{mn} \end{pmatrix} $ **Augmented matrix:** $ [A \mid \mathbf b] = \left[ \begin{array}{cccc|c} a_{11} & a_{12} & \cdots & a_{1n} & b_1 \\ a_{21} & a_{22} & \cdots & a_{2n} & b_2 \\ \vdots & \vdots & \ddots & \vdots & \vdots \\ a_{m1} & a_{m2} & \cdots & a_{mn} & b_m \end{array} \right] $ > [!note] Sometimes augmented matrices do not have the line separating the solutions values and coefficients. # Resources <iframe width="560" height="315" src="https://www.youtube.com/embed/y6bVhgmy2rw?si=zYVdmjo9E1YUJhT2" title="YouTube video player" frameborder="0" allow="accelerometer; autoplay; clipboard-write; encrypted-media; gyroscope; picture-in-picture; web-share" referrerpolicy="strict-origin-when-cross-origin" allowfullscreen></iframe>