Matrix Inverse Calculator (2×2)
Calculate the inverse of a 2×2 matrix, if it exists.
Inv A
0.600000
Formule
## 2×2 Matrix Inverse ### Formula For matrix A = [[a, b], [c, d]] with det ≠ 0: **A⁻¹ = (1/det) × [[d, -b], [-c, a]]** where det = ad - bc. ### Steps 1. Calculate the determinant 2. Swap a and d 3. Negate b and c 4. Divide every element by the determinant ### Verification A × A⁻¹ = I (identity matrix)
Exemple Résolu
Find the inverse of [[4, 7], [2, 6]].
- 01det = 4×6 - 7×2 = 24 - 14 = 10
- 02Inverse = (1/10) × [[6, -7], [-2, 4]]
- 03= [[0.6, -0.7], [-0.2, 0.4]]
Questions Fréquentes
What is a matrix inverse?
The inverse of matrix A is the matrix A⁻¹ such that A × A⁻¹ = I (identity). It "undoes" the transformation represented by A.
When does a matrix have no inverse?
A matrix has no inverse when its determinant is zero. Such matrices are called singular.
Why is the matrix inverse useful?
Matrix inverses are used to solve systems of linear equations (x = A⁻¹b), in computer graphics for inverse transformations, and in statistics for regression analysis.
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