Matrix Multiplication: (2×2) by (2×3)

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Introduction

Suppose we have a 2×2 matrix A, which has 2 rows and 2 columns:

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

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

This results in a 2×3 matrix.

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

Example 1

Suppose we have a 2×2 matrix C, which has 2 rows and 2 columns:

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

Here is how to multiply matrix C by matrix D:

This results in the following matrix:

Example 2

Suppose we have a 2×2 matrix E, which has 2 rows and 2 columns:

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

Here is how to multiply matrix E by matrix F:

This results in the following matrix:

Example 3

Suppose we have a 2×2 matrix G, which has 2 rows and 2 columns:

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

Here is how to multiply matrix G by matrix H:

This results in the following matrix:

Matrix Calculator

The examples above illustrated how to multiply 2×2 matrices by hand. A good way to double check your work if you’re multiplying matrices by hand is to confirm your answers with a matrix calculator. While there are many matrix calculators online, the simplest one to use that I have come across is this one by Math is Fun.

Multiplying Matrices Video Tutorial: (2×2) by (2×3)

https://www.youtube.com/watch?v=yeKJbi8-heE