Introduction to Matrices and Determinants - SS3 Mathematics Lesson Note

A set of numbers arranged in rows and columns to form a rectangular array enclosed within large brackets is called a matrix (plural: matrices). The quantities in the matrix are elements or entries.

A matrix of 2 rows and 3 columns is said to be of order \(2 \times 3\) (read as 2 by 3). Example: \(\begin{bmatrix} 5 & 0 & 2 \\ 4 & 6 & - 1 \\ \end{bmatrix}\). In general, a matrix with \(\mathbf{m - rows}\) and \(\mathbf{n - columns}\) is said have an order of \(m \times n\) read as a \(m\ by\ n\) matrix. Matrices are usually denoted by a capital letter and the entries by a small letter.

\(A = \begin{bmatrix} a_{11} & a_{12} \\ a_{21} & a_{22} \\ \end{bmatrix}\), where \(a_{mn}\) is the entry at the \(m^{th}\)row and \(n^{th}\)column