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A matrix is a rectangular array of numbers arranged in rows and columns. Matrices are fundamental in linear algebra, used for solving systems of equations, 3D computer graphics, machine learning (neural networks), quantum mechanics, and engineering.

ステップバイステップガイド

1. 1Matrix addition/subtraction: add corresponding elements (matrices must be same size)
2. 2Matrix multiplication: row × column dot products (A must have same columns as B has rows)
3. 3Determinant (2×2): det(A) = ad − bc for [[a,b],[c,d]]
4. 4Transpose: flip rows and columns (rows become columns)
5. 5Inverse (2×2): A⁻¹ = (1/det) × [[d,−b],[−c,a]]

解いた例