Problem 72 - College Algebra

Question

Describe how to multiply matrices.

Step-by-Step Solution

Answer

Multiplying matrices involves creating a result matrix where each entry is obtained by multiplying every element in a row of the first matrix by the corresponding element in the column of the second matrix, summing up the results.

Step 1: Ensure correct matrix dimensions

Check the dimensions of the matrices to be multiplied. If a matrix A has dimensions 'm by n', and a matrix B has dimensions 'p by q', then 'n' (the number of columns in A) must equal 'p' (the number of rows in B) for the multiplication to be possible.

Step 2: Initiate a result matrix

Create a result matrix with dimensions 'm by q' (this means it has the same number of rows as the first matrix and the same number of columns as the second one). This matrix will store the result of the multiplication.

Step 3: Carry out the multiplication and addition step

For each entry in the result matrix, multiply every element in a row of the first matrix by the corresponding element in the column of the second matrix, adding up the results. The resultant value is the corresponding entry in the result matrix.

Step 4: Fill the result matrix

Repeat step 3 for all rows of the first matrix and all columns of the second matrix to complete all entries in the result matrix.