Math & Algebra Tool
Matrix Determinant
Calculate determinant of 2x2 and 3x3 matrices.
Input Matrix
Frequently Asked Questions
What is a matrix determinant?+
The determinant is a scalar value calculated from a square matrix. It provides important geometric properties, such as the scaling factor of the linear transformation described by the matrix.
What if the determinant is zero?+
If the determinant is zero, the matrix is 'singular'. This means it does not have an inverse, and the system of equations it represents has either no solution or infinite solutions.
How do you calculate a 2x2 determinant?+
For a matrix [[a, b], [c, d]], the determinant is (a*d) - (b*c). It is the product of the main diagonal minus the product of the other diagonal.
What is the geometric meaning of the determinant?+
In 2D, the absolute value of the determinant represents the area of the parallelogram formed by the column vectors. In 3D, it represents the volume of the parallelopiped.
Can I find the determinant of a non-square matrix?+
No, determinants are only defined for square matrices (where the number of rows equals the number of columns).
Why is the determinant important for eigenvalues?+
Eigenvalues are found by solving the characteristic equation: det(A - λI) = 0. The determinant helps us find these special scalar values essential for stability analysis and physics.