 # Chapter 2 Systems of Linear Equations and Matrices Section 2.4 Multiplication of Matrices.

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Chapter 2 Systems of Linear Equations and Matrices Section 2.4 Multiplication of Matrices

Writing Systems of Equations in Abbreviated Form Consider the following system of equations with three unknowns. Consider the following system of equations with three unknowns. 2x + y – z = 2 x + 3y + 2z = 1 x + 3y + 2z = 1 x + y + z = 2 x + y + z = 2 This system can be written in an abbreviated form as

What is a Matrix? A matrix is a rectangular array of numbers enclosed by brackets. A matrix is a rectangular array of numbers enclosed by brackets. Each number in the array is an element or entry. Each number in the array is an element or entry. An augmented matrix separates the constants in the last column of the matrix from the coefficients of the variables with a vertical line. An augmented matrix separates the constants in the last column of the matrix from the coefficients of the variables with a vertical line.

Classifications of Matrices Often named with capital letters. Often named with capital letters. Classified by size (the number of rows and columns they contain). Classified by size (the number of rows and columns they contain). A matrix with m rows and n columns is an m x n matrix. The number of rows is always given first. A matrix with m rows and n columns is an m x n matrix. The number of rows is always given first.

Special Types of Matrices A matrix with the same number of rows as columns is called a square matrix. A matrix with the same number of rows as columns is called a square matrix. A matrix containing only one row is called a row matrix or a row vector. A matrix containing only one row is called a row matrix or a row vector. A matrix of only one column is a column matrix or a column vector. A matrix of only one column is a column matrix or a column vector.

Scalar Multiplication When determining the product of a real number and a matrix, the real number is called a scalar. When determining the product of a real number and a matrix, the real number is called a scalar.

Example Find the product of each of the following. Find the product of each of the following. 1.) -5A2.) 2B

Matrix Multiplication

Example

Solution

Answer Notice that when you multiply a 2 X 3 matrix with a 3 X 1 matrix, the product is a 2 X 1 matrix.

Another Example

Solution