Calculadora de Matrizes Online Grátis
Matrix addition, subtraction, multiplication, determinant and inverse operations
The Matrix Calculator performs addition, subtraction, and multiplication on matrices of any compatible dimensions, and computes the determinant and inverse of square matrices. It accepts matrices up to a practical size and shows intermediate steps. Linear algebra students, data science practitioners, and engineers solving systems of equations use matrix operations constantly.
Frequently Asked Questions
Sobre Esta Calculadora
Matrices are rectangular arrays of numbers that represent linear transformations, systems of equations, and data tables simultaneously. Matrix addition requires identical dimensions; multiplication requires that the number of columns in the first matrix equals the number of rows in the second. These rules make matrices both powerful and precise.
The determinant of a square matrix indicates whether the matrix is invertible (non-zero determinant) or singular (zero determinant). The inverse of matrix A, written A⁻¹, satisfies A×A⁻¹ = I (identity matrix) and is used to solve the matrix equation Ax = b for x. This is equivalent to solving a system of linear equations.
Matrix operations are fundamental in computer graphics (rotation and scaling transforms), machine learning (weight matrices in neural networks), physics (quantum mechanics and rotation groups), economics (input-output models), and statistics (covariance matrices and multivariate analysis).
Cálculo linear de álgebra nas matrizes.
Exemplo Resolvido
Multiplying two 2×2 matrices
Entradas:
- Matrix A: [[2, 3], [1, 4]]
- Matrix B: [[5, 1], [2, 6]]
Passo a Passo:
- Matrix multiplication: C[i][j] = Σ A[i][k] × B[k][j]
- C[1][1] = 2×5 + 3×2 = 10 + 6 = 16
- C[1][2] = 2×1 + 3×6 = 2 + 18 = 20
- C[2][1] = 1×5 + 4×2 = 5 + 8 = 13
- C[2][2] = 1×1 + 4×6 = 1 + 24 = 25