1. The problem is to understand the definition of a matrix and see some examples. 2. A matrix is a rectangular array of numbers arranged in rows and columns. It is usually denoted by a capital letter such as $A$, $B$, or $C$. 3. The size or dimension of a matrix is given by the number of rows and columns it has, written as $m \times n$, where $m$ is the number of rows and $n$ is the number of columns. 4. For example, a matrix $A$ with 2 rows and 3 columns looks like this: $$ A = \begin{bmatrix} 1 & 2 & 3 \\ 4 & 5 & 6 \end{bmatrix} $$ Here, $A$ is a $2 \times 3$ matrix. 5. Another example is a square matrix, where the number of rows equals the number of columns, such as a $3 \times 3$ matrix: $$ B = \begin{bmatrix} 7 & 8 & 9 \\ 1 & 2 & 3 \\ 4 & 5 & 6 \end{bmatrix} $$ 6. Matrices are used in many areas of mathematics, physics, computer science, and engineering to represent data, perform transformations, and solve systems of equations. 7. Important rules: - Elements of a matrix are usually numbers but can be other mathematical objects. - Matrices can be added or multiplied under certain conditions related to their dimensions. This explanation covers the definition and examples of matrices.