Determinants

User:

Matrices
Algebra
Geometry
Graphs and functions
Trigonometry
Coordinate geometry
Combinatorics

Suma y resta

Producto por escalar

Producto

Inversa

Monomials	Polynomials	Special products	Equations	Quadratic equations
Radical expressions	Systems of equations	Sequences and series	Inner product	Exponential equations
Matrices	Determinants	Inverse of a matrix	Logarithmic equations	Systems of 3 variables equations

Graphs	Definition of slope	Positive or negative slope	Determine slope of a line	Equation of a line	Equation of a line (from graph)
Quadratic function	Parallel, coincident and intersecting lines		Asymptotes	Limits	Distances
	Continuity and discontinuities

Pythagorean Theorem	Sine	Cosine	Tangent	Cosecant	Secant	Cotangent	Trigonometric identities
Trigonometric functions of an acute angle	Trigonometric functions of related angles			Solving right triangles		Law of cosines	Law of sines

Equations of a straight line

Parallel, coincident and intersecting lines

Distances

Angles in space

Inner product

Factorial	Variations without repetition	Variations with repetition	Permutations with repetition	Permutations without repetition
Exercises	Circular permutations	Binomial coefficient	Combinations with repetition	Combinations without repetition

	Arithmetic mean

Determinants

The symbol $A=\left|\begin{matrix}a_{11}&a_{12}&a_{13}\\a_{21}&a_{22}&a_{23}\\a_{31}&a_{32}&a_{33}nd{matrix}\right|$ is a determinant of third order that consists of nine numbers arranged in three rows and three columns.
By definition, the value of a determinant of third order is given by:

|A| = a₁₁a₂₂a₃₃+a₁₃a₂₁a₃₂+a₁₂a₂₃a₃₁-a₁₃a₂₂a₃₁-a₁₂a₂₁a₃₃-a₁₁a₂₃a₃₃

and is called the expansion of the determinant.

To remember easily, you can use:

Express the value of the determinant:

-9	-1	2
-1	3	-5
1	-1	2