
Matrices—Operations and Inverses 
Lesson Objective In this lesson, you will review matrices and their operations. You will also identify the properties of operations on matrices and explore inverses. 
Matrices A matrix is a rectangular array of numbers. The numbers in a matrix are referred to as the elements of a matrix. A matrix is made up of rows and columns. The dimensions of the matrix are said to be “m by n” which is written m × n. An m × n matrix has m rows and n columns. This notation does not mean that you multiply m by n. A 1 × n matrix is sometimes called a row vector. A m × 1 matrix is sometimes called a column vector. Let A is a 3 × 2 matrix, while both B and C are 2 × 2 matrices. The number 2 is the entry for a_{11}, b_{21}, b_{22}, and c_{12}. Two matrices A and B are equal if A and B have the same dimensions, and every entry a_{ij} is equal to every entry b_{ij}. The two matrices P and Q shown below are equal. Notice that they are both 2 × 3 matrices and their respective entries are equal to each other. 


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