Matrix Determinant Calculator

What is the Determinant Of a Matrix?

The determinant of a square matrix is a scalar value that provides important information about the matrix, including whether it is invertible and the volume scaling factor of the linear transformation it represents.

Key Properties of Determinants:

1. Invertibility: A matrix is invertible if and only if its determinant is non-zero.
2. Volume Scaling: The absolute value of the determinant represents the factor by which the matrix scales volumes in linear transformations.
3. Product of Eigenvalues: The determinant is the product of the eigenvalues of the matrix.
4. Multiplicative Property: det(AB) = det(A)det(B).
5. Transpose Invariance: det(A^T) = det(A)

About Matrix Determinant Calculator

The Matrix Determinant Calculator calculates the determinant of a matrix. Only square matrices can have determinants.

Features

The Matrix Determinant Calculator has the following features:

• Supports matrices of sizes 2×2, 3×3 and 4×4.
• Entries are filled with random quantities for quick testing.
• Quick calculation and mobile-friendly responsive design.

Uses

The Matrix Determinant Calculator has the following uses:

• Used to find determinant of a matrix.
• Used to test the invertibility of a matrix(if determinant is non zero then matrix is invertible).
• Used to solve linear equations by the Cramer’s Rule.

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