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Matrices & determinants formulas
11 formulas for Matrices & determinants, from the Algebra section of the Quantix formula library. Tap 🧮 next to a formula to solve it for any variable with step-by-step working.
| Name | Formula | Note |
|---|---|---|
| 2×2 determinant | |a b; c d| = ad − bc | |
| 3×3 determinant | a(ei − fh) − b(di − fg) + c(dh − eg) | rows (a b c), (d e f), (g h i) |
| Inverse of 2×2 | A⁻¹ = (1/(ad − bc)) [d −b; −c a] | |
| Inverse | A⁻¹ = adj(A) / |A| | |A| ≠ 0 |
| Transpose of product | (AB)ᵀ = BᵀAᵀ | |
| Inverse of product | (AB)⁻¹ = B⁻¹A⁻¹ | |
| Determinant of product | |AB| = |A||B| | |
| Scalar multiple | |kA| = kⁿ|A| | n × n matrix |
| Adjoint | |adj A| = |A|ⁿ⁻¹ | |
| Cramer's rule | x = Dₓ/D, y = D_y/D, z = D_z/D | |
| Area of triangle | ½ |x₁(y₂ − y₃) + x₂(y₃ − y₁) + x₃(y₁ − y₂)| |
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