Determinant Formula

Determinant Formula

Determinant in linear algebra is a useful value which is computed from the elements of a square matrix. The determinant of a matrix A is denoted det (A), det A, or |A|. It is a function that has an input accepts

n×n
matrix and output in a real or a complex number which is called as the determinant of the input matrix. Determinants occur throughout mathematics. For example, a matrix is often used to represent the coefficients in a system of linear equations, and the determinant is used to solve these equations, even though more efficient techniques are actually used, some are determinant-revealing and consist of computationally effective ways of calculating the determinant itself.

If A=[abcd]

The Determinant Formula is

 Determinant=ad−bc

If B=[ijkabcxyz]

The Determinant Formula is

Determinant=i(bz−cy)−j(az−cx)+k(ay−bx)

Solved Examples

Question 1: Find out the determinant of 

[4278]

Solution:

Given 2
×
 2 matrix is,

A =

[4278]

Determinant is calculated as,

ad – bc = (4

×
 8) â€“ (2
×
7) = 32 – 14 = 18

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