Explanation

A matrix is a rectangular array of numbers. Dimensions: rows × columns. A 2×3 matrix has 2 rows and 3 columns. Elements identified by position: a₁₂ is row 1, column 2.

Addition: add corresponding elements (matrices must have same dimensions). Scalar multiplication: multiply every element by the scalar. Matrix multiplication: row × column = sum of products.

Applications: solving systems of equations, transformations in graphics, data organization, network analysis. Matrices enable efficient computation with large datasets.