Linear Algebra
Matrix Multiplication - Linear Algebra
Learn the matrix multiplication with examples, step-by-step guide, and calculator tools. Multiply matrices using dot product
The matrix multiplication is a fundamental concept in linear algebra. Multiply matrices using dot product. This page provides a comprehensive guide with worked examples and practical applications.
The Formula
\[[AB]_{ij} = \sum_{k=1}^{n} A_{ik}B_{kj}\]
Variables
n
Number of columns in A (rows in B)
Step-by-Step Guide
- 1
Step 1: Gather your data values
- 2
Step 2: Apply the formula
- 3
Step 3: Perform the calculations
- 4
Step 4: Interpret the result
Examples
Example 1
Example 1: [] → [1 2; 3 4] × [5 6; 7 8] = [19 22; 43 50]
Example 2
Example 2: [19 22; 43 50]
Frequently Asked Questions
What is the matrix multiplication?
Multiply matrices using dot product
How do I calculate matrix multiplication?
Use the formula: [AB]_{ij} = \sum_{k=1}^{n} A_{ik}B_{kj}. Follow the steps provided above.
What tools can help with matrix multiplication?
We provide online calculators: calculator