In these lessons, we will learn how to perform matrix multiplication. We will illustrate matrix multiplication or matrix product by the following example. Example: Find C = A × B. Solution: Step 1: Multiply the elements in the first row of A with the corresponding elements in the first column of B. Add the products to get the element C 11. Step 1: accept two matrix by declaring two variables. Step 2: assign 3 rd variable for output and write a statement as matrix 1. matrix 2. Step 3: display output. Using ‘mtimes' Command. In this method, there is no need for operators we can give the direct command to the input matrix. A statement can be written as mtimes ( matrix 1, matrix 2 ). The main condition of matrix multiplication is that the number of columns of the 1st matrix must equal to the number of rows of the 2nd one. As a result of multiplication you will get a new matrix that has the same quantity of rows as the 1st one has and the same quantity of columns as the 2nd one. Consider two matrices A and B. If A is an m x n matrix and B is an n x p matrix, they could be multiplied together to produce an m x n matrix C. Matrix multiplication is possible only if the number of columns n in A is equal to the number of rows n in B.
Introduction
Suppose we have a 3×3 matrix A, which has 3 rows and 3 columns:
| A = |
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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:
| A x B = |
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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:
| D = |
|
Here is how to multiply matrix C by matrix D:
| C x D = |
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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:
| E = |
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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: Apngtogifconverter 3 3 0.
| E x F = |
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This results in the following 3×2 matrix:
Example 3
A text 2 35 56. Suppose we have a 3×3 matrix G, which has 3 rows and 3 columns:
| G = |
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3 X 1 Matrix Multiplication
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:
| G x H = |
|
This results in the following 3×2 matrix:
Matrix Calculator
The examples above illustrated how to multiply 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 (3×3) by (3×2)
Here you can perform matrix multiplication with complex numbers online for free. However matrices can be not only two-dimensional, but also one-dimensional (vectors), so that you can multiply vectors, vector by matrix and vice versa.
After calculation you can multiply the result by another matrix right there!
Have questions? Read the instructions.
About the method
- The main condition of matrix multiplication is that the number of columns of the 1st matrix must equal to the number of rows of the 2nd one.
- As a result of multiplication you will get a new matrix that has the same quantity of rows as the 1st one has and the same quantity of columns as the 2nd one.
- For example if you multiply a matrix of 'n' x 'k' by 'k' x 'm' size you'll get a new one of 'n' x 'm' dimension.
Multiplication Facts 0 1 2
To understand matrix multiplication better input any example and examine the solution.
