Calculadora de Matriz Inversa 2×2
Encuentra la matriz inversa de una matriz 2×2. Ingresa los elementos y obtén la inversa con el procedimiento completo al instante.
Inv A
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Fórmula
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)
Ejemplo Resuelto
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]]
Preguntas Frecuentes
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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