Phần hướng dẫn bên dưới chưa có bằng tiếng Việt nên được hiển thị bằng tiếng Anh. Bản thân máy tính đã được dịch đầy đủ.
Cách sử dụng máy tính này
- Choose an operation.
- Set the number of rows and columns and type the entries. Decimals and negative numbers are allowed.
- The result updates as you type.
Công thức
Matrix multiplication takes dot products of rows of A with columns of B, so A's column count must equal B's row count. Determinants and inverses use Gaussian elimination with partial pivoting for numerical stability.
(AB)ᵢⱼ = Σₖ Aᵢₖ Bₖⱼ
det(A) = product of pivots × (−1)^(row swaps)
A⁻¹ exists only if det(A) ≠ 0
2 × 2 example
- A = [[4, 7], [2, 6]].
- det(A) = 4 × 6 − 7 × 2 = 10.
- A⁻¹ = (1/10) × [[6, −7], [−2, 4]] = [[0.6, −0.7], [−0.2, 0.4]].
Câu hỏi thường gặp
Is matrix multiplication commutative?
No. In general AB ≠ BA, and one product may exist while the other doesn't.
Why can't my matrix be inverted?
A matrix with determinant 0 is singular: its rows are linearly dependent, so no inverse exists.
What is the rank of a matrix?
The number of linearly independent rows (or columns). A square n × n matrix is invertible exactly when its rank is n.