Matrix Determinant (2×2 & 3×3) कैलकुलेटर — मुफ़्त ऑनलाइन टूल और फॉर्मूला
Computes determinants for 2×2 and 3×3 square matrices with explicit Laplace cofactor expansions and geometric singularity checks.
Invertibility: Invertible / Non-Singular (det ≠ 0)
फॉर्मूला और गणना की विधि
Calculates the determinant scalar of square matrices via Laplace cofactor expansion, measuring the geometric scaling factor of linear transformations.
वेरिएबल परिभाषाएँ और माप इकाइयाँ
Determinant of 3×3 Matrix
Computing det for row1 [1, 2, 3], row2 [0, 1, 4], row3 [5, 6, 0].
Geometric Meaning of the Determinant
In 2D space, the absolute value of the determinant represents the area of the parallelogram formed by the column vectors. In 3D space, it represents the volume of the parallelepiped.
If det(A) = 0, the transformation collapses dimensions (squashing 3D space into a 2D plane or line), meaning the transformation has no inverse.
Matrix Determinant (2×2 & 3×3) कैलकुलेटर से जुड़े अक्सर पूछे जाने वाले प्रश्न
What does a negative determinant mean?
A negative determinant indicates that the linear transformation reverses the spatial orientation (e.g. reflects like a mirror).
Can a non-square matrix have a determinant?
No. Determinants are exclusively defined for square matrices (n × n).
संबंधित ऑनलाइन कैलकुलेटर
Matrix Determinant (2×2 & 3×3) कैलकुलेटर के साथ अक्सर संदर्भित अन्य कैलकुलेटर।
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