Determinant of Matrix Formulas
Determinant of any matrix can easily be claulated using the Determinnat Formulas, For any 2×2, 3×3, or any n×n matrices its deteminat is calculated below,
Determinant of 2×2 Matrix
For a 2×2 matrix
det(A) is given by:
det(A) = ad − bc
Example: Find determinant of
Solution:
Determinant of A = |A|
|A| = (1.4) – (2.3)
|A| = 4 – 6
Determinant of 3×3 Matrix
For a 3×3 matrix
A =
Determinant is given by
det(A) = a(ei-fh) – b(di-fg) + c(dh-eg)
Example: Find determinant of
Solution:
Determinant of A = |A|
|A| = 0
Learn more about, Determinant of 3×3 Matrix
Determinant of a n×n Matrix
When calculating the determinant of a n×n matrix (n > 3), more intricate calculations are required. Typically, techniques like cofactor expansion, expansion by minors, or block matrix characteristics are used. Recursive in nature, the general formula can be somewhat complex.
A popular method is to write the determinant as the product of elements and the cofactors that go with them.
where the element in the i-th row and j-th column of matrix C is represented by the symbol Cij.
Determinant of 2×2 Matrix
Determinant of a 2×2 Matrix A = is denoted as |A| and is calculated as |A| = [ad – bc]. It is used in solving various problems related to a matrix and is used in finding the Inverse, and Rank of 2×2 Matrix.
In this article, we will learn about, the Determinant of Matrix, Determinant of 2×2 Matrix, Examples, and others in detail.
Table of Content
- What is Determinant of a Matrix?
- Determinant of a 2×2 Matrix
- How to Calculate Determinant of a 2×2 Matrix
- Determinant of Inverse of a Matrix
- Application of Determinant of 2×2 Matrix
- Examples of Determinant of 2×2 Matrix