Determinant of Matrix
What is meant by the determinant formula?
For any 3×3 matrix A = [Tex]\begin{bmatrix} a & b & c \\ d & e & f \\ g & h & i \end{bmatrix} \\ [/Tex] the shortcut formula for computing its determinant is:
|A| = a (ei − fh) − b (di − fg) + c (dh − eg)
Can determinant of any matrix be negative?
Yes, the determinant of any matrix can be negative.
Can determinant of any matrix ever be equal to 0?
Yes, the determinant of any matrix can be zero if any one row or column of the matrix has all the zero values. It can also be zero if any two rows or columns of the matrix are equal.
How to find the determinant of matrix?
The determinant of any matrix can be found by using the following steps:
Step 1: Select any row or column of our choice.
Step 2: Calculate the cofactors of all the elements of the selected row or column
Step 3: The product of the elements of the row or column by their corresponding cofactors is found. The calculated product is added with alternate negative sign.
Determinant of a Matrix with Solved Examples
Determinant of a Matrix is defined as the function that gives the unique output (real number) for every input value of the matrix. Determinant of the matrix is considered the scaling factor that is used for the transformation of a matrix. It is useful for finding the solution of a system of linear equations, the inverse of the square matrix, and others. The determinant of only square matrices exists.
Table of Content
- Determinant of Matrix Calculator
- Definition of Determinant of Matrix
- Determinant of a 1×1 Matrix
- Determinant of 2×2 Matrix
- Determinant of a 3×3 Matrix
- Determinant of 4×4 Matrix
- Determinant of Identity Matrix
- Determinant of Symmetric Matrix
- Determinant of Skew-Symmetric Matrix
- Determinant of Inverse Matrix
- Determinant of Orthogonal Matrix
- Physical Significance of Determinant
- Laplace Formula for Determinant
- Properties of Determinants of Matrix