Problem 74 - College Algebra

Question

If two matrices can be multiplied, describe how to determine the order of the product.

Step-by-Step Solution

Answer

The order of the product of two matrices is determined by the number of rows from the first matrix and the number of columns from the second matrix. If the first matrix has dimensions m x n and the second matrix has dimensions p x q, for multiplication to be possible, n must be equal to p. However, the order of the product matrix will be m x q.

Step 1: Understand Matrices Dimension

To start, one needs to understand the dimensions of matrices. A matrix has rows and columns. The dimension of a matrix is given as (Number of Rows) x (Number of Columns).

Step 2: Conditions for Multiplication

Multiplication of two matrices is possible only when the number of columns in the first matrix is equal to the number of rows in the second matrix. If Matrix A has dimensions m x n, and Matrix B has dimensions p x q, then for multiplication to be possible, n (the number of columns in Matrix A) must be equal to p (the number of rows in Matrix B).

Step 3: Determine the Order of the Product

Once multiplication is verified to be possible, the order of the product matrix (Matrix C) is determined by the number of rows from the first matrix (m) and the number of columns from the second matrix (q), resulting into a matrix of order m x q.