Matrix multiplication is a fundamental operation in linear algebra. In this tutorial, we will explore the concept of matrix multiplication and learn how to perform it step by step.

What is Matrix Multiplication?

Matrix multiplication is a method of multiplying two matrices. The resulting matrix is called the product of the two matrices.

Key Points:

  • The number of columns in the first matrix must be equal to the number of rows in the second matrix.
  • The resulting matrix will have the same number of rows as the first matrix and the same number of columns as the second matrix.

Steps to Multiply Matrices

Step 1: Align the Matrices

Align the matrices so that the columns of the first matrix match the rows of the second matrix.

Step 2: Multiply and Sum

For each element in the resulting matrix, multiply the corresponding elements from the first matrix and the second matrix, and then sum them up.

Example

Let's multiply two matrices:

Matrix A:
1 2
3 4

Matrix B:
5 6
7 8

The resulting matrix C will be:

Matrix C:
(1*5 + 2*7)  (1*6 + 2*8)
(3*5 + 4*7)  (3*6 + 4*8)

Practice

Try multiplying the following matrices:

Matrix A:
2 3
4 5

Matrix B:
1 2
3 4

For more information and practice exercises, check out our Matrix Multiplication Practice.

Matrix

Conclusion

Matrix multiplication is a powerful tool in linear algebra. Understanding how to perform matrix multiplication is essential for many applications, such as computer graphics, physics, and engineering.