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Linear Algebra
University
Linear Algebra (University Level)
2×2 Matrix Inverse
Find the inverse of a 2×2 matrix
Standard Formula
A⁻¹ = (1/det) × [d -b; -c a], det = ad - bc
Interactive Sandbox
Live Reactive
Adjust values in real-time and observe mathematical cause-and-effect
a
120
b
121
c
120
d
120
Live EquationFormula Proof
A⁻¹ = (1/det) × [6 -7; -2 4], det = ad - bc = 0.6
Dynamic Formula Model
Calculated Solution
0.6
Direct computational model evaluating 2×2 Matrix Inverse.
Variable Mechanics
Roles, constraints & impacts
4 Params
a
A₁₁
A₁₁
ImpactPrimary formula parameter
ConstraintReal number
b
A₁₂
A₁₂
ImpactPrimary formula parameter
ConstraintReal number
c
A₂₁
A₂₁
ImpactPrimary formula parameter
ConstraintReal number
d
A₂₂
A₂₂
ImpactPrimary formula parameter
ConstraintReal number
At a Glance
Gotchas, units & real-world use
Essential
Formula Nature & Mechanics
Direct computational model evaluating 2×2 Matrix Inverse.
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: 2×2 Matrix Inverse
Given:
- a = 4
- b = 7
- c = 2
- d = 6
- det = (4)(6) - (7)(2) = 10
- A⁻¹ = (1/10) × [6 -7; -2 4]
- A⁻¹ = [0.6 -0.7; -0.2 0.4]
Answer: 0.6
Frequently Asked Questions
What is the 2×2 Matrix Inverse formula?
A⁻¹ = (1/det) × [d -b; -c a], det = ad - bc. Find the inverse of a 2×2 matrix.
How do I calculate 2×2 Matrix Inverse?
Enter A₁₁ (a), A₁₂ (b), A₂₁ (c), A₂₂ (d) into the calculator. It applies A⁻¹ = (1/det) × [d -b; -c a], det = ad - bc and shows every step of the working.
Related Linear Algebra Calculators
2×2 Matrix Determinantdet(A) = ad - bcDot Product of Vectorsa · b = a₁b₁ + a₂b₂ + a₃b₃Vector Magnitude|v| = √(x² + y² + z²)Eigenvalues of 2×2 Matrixλ = (a+d ± √((a+d)²-4(ad-bc)))/22×2 Matrix Multiplication[a b; c d] × [e f; g h] = [ae+bg af+bh; ce+dg cf+dh]3×3 Matrix Determinantdet = a(ei - fh) - b(di - fg) + c(dh - eg)
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