Determinant Calculator – Calculate Matrix Determinants
Calculate determinants of 2x2 and 3x3 matrices
Table of Contents
How to Use
- Select matrix size (2x2 or 3x3)
- Enter the matrix elements
- Click calculate to see the determinant
- Review the result with the matrix visualization
What is a Determinant?
A determinant is a scalar value that can be computed from the elements of a square matrix. It provides important information about the matrix, including whether the matrix is invertible and properties of the linear transformation it represents.
Calculation Methods
For a 2x2 matrix [[a,b],[c,d]], the determinant is ad - bc. For 3x3 matrices, we use the rule of Sarrus or cofactor expansion.
Frequently Asked Questions
- What does a determinant of zero mean?
- A determinant of zero means the matrix is singular (non-invertible). The rows or columns are linearly dependent, and the matrix doesn't have full rank.
- How do I calculate a 2x2 determinant?
- For a 2x2 matrix [[a,b],[c,d]], multiply the diagonal elements (a×d) and subtract the product of the off-diagonal elements (b×c): det = ad - bc.