Properties of Determinants Explained | Row Operations, Multiplication & Invertibility

Описание: You’ve learned how to calculate determinants—but what do they do? In this video, we explore the key properties of determinants that make them so powerful in linear algebra.

From how row operations affect determinant values to why det(AB) = det(A)·det(B), this episode gives you the tools to work smarter—not harder—when dealing with determinants.

✅ What You’ll Learn:
• The three row operations and how they change a determinant
• Why swapping rows flips the sign
• Why scaling a row scales the determinant
• Why row addition leaves the determinant unchanged
• The multiplicative property: det(AB) = det(A)·det(B)
• Why a zero determinant means the matrix is not invertible

📌 Part of the Linear Algebra Essentials series →    • Linear Algebra I | Intro to Linear Algebra  

⏱️ Timestamps:
00:00 Intro
00:18 Multiplicative Property (det(AB) = det(A)·det(B))
00:53 Example 1
04:40 Transpose property
06:13 Effects of row operations

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