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Definition: A matrix is a two-dimensional array of numbers or expressions arranged in rows and columns. An m × n matrix A has m rows and n columns and is written as: $$ A = \begin{bmatrix} a_{11} & a_{12} & \cdots & a_{1n} \\ a_{21} & a_{22} & \cdots & a_{2n} \\ \vdots & \vdots & \ddots & \vdots \\ a_{m1} & a_{m2} & \cdots & a_{mn} \end{bmatrix} $$ where the element \( a_{ij} \) is located in the \( i^{th} \) row and the \( j^{th} \) column....