Matrix Multiplication Explained | Step-by-Step Examples

Описание: 📚 Learn How to Multiply Matrices Step-by-Step

In this video, you'll learn how to perform matrix multiplication with clear, guided examples. We’ll begin by showing how to determine if two matrices can be multiplied based on their dimensions, then walk through the process of calculating each element in the product matrix.

You’ll also learn how to square a matrix—that is, multiply a square matrix by itself—and when this operation is defined.

Matrix multiplication is a foundational concept in algebra and linear algebra. Understanding how it works is essential for solving systems of equations, performing transformations, and working with matrix equations.

🔍 What You’ll Learn in This Video:
✅ When You Can Multiply Two Matrices
✔ Matrix dimensions must align: (m × n)(n × p) = (m × p)
✔ The number of columns in the first matrix must equal the number of rows in the second

✅ How to Multiply Two Matrices
✔ Multiply rows by columns using dot products
✔ Calculate each entry a_ij in the resulting matrix
✔ Practice with 2×2, 2×3, and 3×2 matrix examples

✅ How to Square a Matrix
✔ Multiply a matrix by itself: A² = A × A
✔ Only defined when A is a square matrix
✔ Example with a 2×2 matrix

✅ Examples Covered:
✔ Multiply a 2×2 matrix by a 2×2 matrix
✔ Multiply a 2×3 matrix by a 3×2 matrix
✔ Multiply matrices with incompatible dimensions (undefined case)
✔ Find A² for a square matrix

By the end of this video, you’ll be able to:
✔ Decide when matrix multiplication is defined
✔ Perform multiplication accurately
✔ Understand how to square a matrix

📥 Download Free Guided Notes!
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Timestamps
00:00 Introduction
00:29 How to Multiply Two Matrices
02:23 Basic Example
05:50 Other Examples
09:59 Squaring a Matrix

More About Understand The Math
Understand The Math offers clear, accessible, and engaging mathematics instruction for students and lifelong learners. I'm Cheryl Hile, the founder of Understand The Math, with a Ph.D. in Engineering Science and Applied Mathematics and over 25 years of university teaching experience. My goal is to provide accurate, high-quality math instruction through step-by-step explanations and carefully worked-out examples.

Each video includes free guided notes, linked in the description. These notes help students follow along, highlight key concepts, and practice problems, making review easier and more effective.

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