Determinant of a 2×2 Matrix | Simple Formula and Clear Examples

Описание: 📚 Learn How to Find the Determinant of a 2×2 Matrix Using a Simple Formula and Clear Examples

In this video, you’ll learn what a determinant is and how to calculate it for a 2×2 matrix using a straightforward formula. The determinant is a real number that provides key information about a matrix—especially in linear algebra, where it helps determine invertibility and properties of linear systems.

We’ll go over the formula, show how to apply it step-by-step, and work through multiple examples so you can master this foundational skill.

🔍 What You’ll Learn in This Video:
✅ What Is a Determinant?
✔ A value associated with a square matrix
✔ Used in solving systems, checking invertibility, and more
✔ Notation: det(A) or |A|

✅ Determinant of a 2×2 Matrix
✔ Formula: det(A) = ad − bc
✔ Multiply the main diagonal and subtract the product of the off-diagonal
✔ Only defined for square matrices

✅ Examples Covered:
✔ A = [2 5; 3 4] → det(A) = 2(4) − 5(3) = −7
✔ A = [2 5; 4 10] → det(A) = 2(10) − 5(4) = 0

By the end of this video, you’ll be able to:
✔ Apply the determinant formula correctly
✔ Understand what the determinant tells you about a matrix
✔ Compute the determinant of any 2×2 matrix

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Matrices and Determinants
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   • Matrix Multiplication Explained | Step-by-...  
   • Determinant of a 2×2 Matrix | Simple Formu...  
   • Determinant of a 3×3 Matrix | Shortcut Met...  
   • Inverse of a 2×2 Matrix | Simple Formula a...  
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Timestamps
00:00 Introduction
00:17 Determinant Definition
00:53 Formula for a 2x2 Matrix
01:30 Examples

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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