A matrix is a rectangular array of numbers, symbols, or expressions arranged in rows and columns. Each number in the matrix is called an element or entry. This example shows a 3 by 3 matrix with 3 rows and 3 columns.
Matrix dimensions are written as rows times columns. A square matrix has equal rows and columns. A row vector has only one row, while a column vector has only one column. These different types serve various purposes in mathematics and applications.
Matrices can be added together if they have the same dimensions. To add matrices, we simply add the corresponding elements in each position. For example, the element in row 1 column 1 of matrix A is added to the element in row 1 column 1 of matrix B.
Matrix multiplication is more complex than addition. We multiply rows of the first matrix by columns of the second matrix. For example, to get the first element, we multiply 1 times 5 plus 2 times 7, which equals 19. The number of columns in the first matrix must equal the number of rows in the second matrix.
To summarize what we have learned about matrices: A matrix is a rectangular array of numbers arranged in rows and columns. We can add matrices of the same dimensions and multiply matrices following specific rules. Matrices are essential mathematical tools used in many fields including computer science, physics, and engineering.