Basic Operations whit Determinants

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Introduction to Determinants

Determinants: (lesson 1 of 2)

Introduction to Determinant

In the following we assume we have a square matrix $(m=n)$ . The determinant of a matrix $A$ will be denoted by $\det(A)$ or $|A|$ .

Determinant of a 2 $\times$ 2 matrix

Assuming $A$ is an arbitrary 2 $\times$ 2 matrix $A$ , where the elements are given by: $A = \left( {} \right)$

then the determinant of this matrix is as follows:

$\det (A) = \left| A \right| = \left| {} \right| = {a_{11}}{a_{22}} - {a_{21}}{a_{12}}$

Determinant of a 3 $\times$ 3 matrix

The determinant of a 3 $\times$ 3 matrix is a little more tricky and is found as follows ( for this case assume $A$ is an arbitrary 3 $\times$ 3 matrix $A$ , where the elements are given below)

$A = \left( {} \right)$

then the determinant of this matrix is as follows:

$\det (A) = \left| {} \right| = {a_{11}}\left| {} \right| - {a_{12}}\left| {} \right| + {a_{13}}\left| {} \right|$

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Introduction to Determinant

Determinant of a 2 ×\times× 2 matrix

Determinant of a 3 ×\times× 3 matrix

Algebra

Calculus

Analytic geometry

Linear Algebra

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Determinant of a 2 $\times$ 2 matrix

Determinant of a 3 $\times$ 3 matrix