免费逆矩阵计算器
计算2x2矩阵的逆矩阵。
Inv A
0.600000
公式
## 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)
计算示例
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]]
常见问题
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.
学习