3×3 Matrix Determinant
Calculate the determinant of a 3×3 matrix
Interactive Sandbox
Adjust values in real-time and observe mathematical cause-and-effect
Direct computational model evaluating 3×3 Matrix Determinant.
Variable Mechanics
Roles, constraints & impacts
A₁₁
A₁₁
A₁₂
A₁₂
A₁₃
A₁₃
A₂₁
A₂₁
A₂₂
A₂₂
A₂₃
A₂₃
A₃₁
A₃₁
A₃₂
A₃₂
A₃₃
A₃₃
At a Glance
Gotchas, units & real-world use
Formula Nature & Mechanics
Direct computational model evaluating 3×3 Matrix Determinant.
Common Mistakes & Traps
- Ensure all input measurements share consistent units before calculating.
- Check for denominator values approaching zero to prevent undefined division.
- Follow standard order of operations (PEMDAS: Parentheses, Exponents, Multiply/Divide, Add/Subtract).
Dimensional Analysis & Units
Direct evaluation matching formula variable dimensions.
Real-World & Industry Application
Widely utilized across modern linear algebra applications, academic analysis, and engineering estimations.
Worked Example: 3×3 Matrix Determinant
Given:
- a = 6
- b = 1
- c = 1
- d = 4
- e = -2
- f = 5
- g = 2
- h = 8
- i = 7
- det = 6(-2×7 - 5×8) - 1(4×7 - 5×2) + 1(4×8 - (-2)×2)
- det = 6(-54) - 1(18) + 1(36)
- det = -324 - 18 + 36
- det = -306
Answer: -306
Frequently Asked Questions
What is the 3×3 Matrix Determinant formula?
det = a(ei - fh) - b(di - fg) + c(dh - eg). Calculate the determinant of a 3×3 matrix.
How do I calculate 3×3 Matrix Determinant?
Enter A₁₁ (a), A₁₂ (b), A₁₃ (c), A₂₁ (d), A₂₂ (e), A₂₃ (f), A₃₁ (g), A₃₂ (h), A₃₃ (i) into the calculator. It applies det = a(ei - fh) - b(di - fg) + c(dh - eg) and shows every step of the working.
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