Algebra and Trigonometry, 5th Edition

9.4 Matrix Operations

• Add, subtract, and multiply matrices when possible.

• Write a matrix equation equivalent to a system of equations.

In addition to solving systems of equations, matrices are useful in many other types of applications. In this section, we study matrices and some of their properties.

A capital letter is generally used to name a matrix, and lower-case letters with double subscripts generally denote its entries. For example, $a_{47}$, read “a sub four seven,” indicates the entry in the fourth row and the seventh column. A general term is represented by $a_{ij}$. The notation $a_{ij}$ indicates the entry in row i and column j. In general, we can write a matrix as

$$\mathbf{\text{A}}=[a_{ij}]=\left[\begin{array}{ccccc}{a}_{11}& a_{12}& a_{13}& \cdots & a_{1n}\\ a_{21}& a_{22}& a_{23}& \cdots & a_{2n}\\ a_{31}& a_{32}& a_{33}& \cdots & a_{3n}\\ ⋮& ⋮& ⋮& ⋮\\ a_{m1}& a_{m2}& a_{m3}& \cdots & a_{mn}\end{array}\right].$$

The matrix ...