Matrix Multiplication: (3×3) by (3×2)

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Introduction

Suppose we have a 3×3 matrix A, which has 3 rows and 3 columns:

Suppose we also have a 3×2 matrix B, which has 3 rows and 2 columns:

To multiply matrix A by matrix B, we use the following formula:

This results in a 3×2 matrix.

The following examples illustrate how to multiply a 3×3 matrix with a 3×2 matrix using real numbers.

Example 1

Suppose we have a 3×3 matrix C, which has 3 rows and 3 columns:

Suppose we also have a 3×2 matrix D, which has 3 rows and 2 columns:

Here is how to multiply matrix C by matrix D:

This results in the following 3×2 matrix:

Example 2

Suppose we have a 3×3 matrix E, which has 3 rows and 3 columns:

Suppose we also have a 3×2 matrix F, which has 3 rows and 2 columns:

Here is how to multiply matrix E by matrix F:

This results in the following 3×2 matrix:

Example 3

Suppose we have a 3×3 matrix G, which has 3 rows and 3 columns:

Suppose we also have a 3×2 matrix H, which has 3 rows and 2 columns:

Here is how to multiply matrix G by matrix H:

This results in the following 3×2 matrix:

Additional Resources

The following tutorials explain how to perform other common matrix multiplications:

Matrix Multiplication: (2×2) by (2×2)
Matrix Multiplication: (2×2) by (2×3)