Matrix Determinant Calculator
Calculate the determinant of 2x2, 3x3, and 4x4 matrices with ease. Enter your matrix and get instant results.
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What is a Matrix Determinant?
In linear algebra, the determinant of a square matrix is a scalar value that can be computed from the elements of a square matrix. The determinant of a matrix A is denoted as det(A), det A, or |A|. It is a fundamental concept and has various applications in mathematics, physics, and engineering.
Use Cases:
- Determining if a matrix is invertible.
- Solving systems of linear equations using Cramer's rule.
- Calculating eigenvalues and eigenvectors.
- In geometry, determinants are used to find the area or volume scaling factor of linear transformations.
Formula for Determinants:
For a 2x2 matrix $$ A = \begin{pmatrix} a & b \\ c & d \end{pmatrix} $$, the determinant is calculated as: $$ det(A) = ad - bc $$.
For a 3x3 matrix, the formula is more complex and involves expanding along a row or column. For larger matrices, computational methods are typically used.
Source: Wikipedia - Determinant