Algebra 3: Section 5.5 Objectives of this Section Find the Sum and Difference of Two Matrices Find Scalar Multiples of a Matrix Find the Product of Two Matrices Find the Inverse of a Matrix Solve Systems of Equations Using Inverse Matrices

A matrix with m rows and n columns is called an m by n matrix.

Note that in order for two matrices to be combined with addition or subtraction, they must have the same number of rows and columns.

If k is a real number and A is an m by n matrix, the matrix kA is

Let A denote an m by r matrix and let B denote an r by n matrix. The product AB is defined as the m by n matrix whose entry in row i, column j is the product of the ith row of A and the jth column of B.

Continue performing row operations on the augmented matrix until the matrix on the left is the identity matrix.

If a matrix represents the coefficients of a linear system of equations, the inverse matrix can be used to solve the system.