**App Name (Nome App)**: ALG Math Solver

**Operating System (Sistema Operativo)**: iOS

**Developer (Sviluppatore)**: ALG Software Lab

**App Category (Categoria)**: Istruzione

**Price (Prezzo)**: Free - Gratis

The app is intended for students and engineers and anyone who uses mathematical calculations in their studies or work.

The application contains more than 100 calculators for solving various problems in linear algebra, matrix calculations, analytical geometry, elementary geometry, systems of linear equations, quadratic equations and much more. Each calculator contains a small theory on a specific task.

The program, using the necessary formulas, will perform step-by-step calculations and display a detailed solution.

This app also includes a random number generator to quickly create sample expressions with random numbers.

The application performs the following operations:

Matrix operations, Determinants

Matrix addition

Matrix subtraction

Matrix multiplication

Matrix multiplication by scalar

Matrix transpose

Matrix square

Determinant: Sarrus method

Determinant: Laplace method

Invertible matrix

Vector Calculus

Vector Length

Vector coordinates by two points

Vectors addition

Vectors subtraction

Scalar and vector multiplication

Scalar product of vectors

Cross product of vectors

Mixed triple product

Angle between two vectors

Projection of a vector onto another vector

Direction cosines

Collinear vectors

Orthogonal vectors

Coplanar vectors

Area of triangle formed by vectors

Area of a parallelogram formed by vectors

Volume of pyramid formed by vectors

Volume of a parallelepiped formed by vectors

Analytic geometry, 2D

General equation of a straight line

Slope equation of a straight line

Line equation in segments

Polar parameters of the line

Relationship between line and point

Distance between two points

Dividing a segment in half

Dividing a segment in a given ratio

Triangle area

Condition under which three points lie on the same line

Condition of parallel lines

Two lines are perpendicular

Angle between two lines

Bunch of lines

Relationship between a line and a pair of points

Point to line distance

Analytic geometry, 3D:

Equation of a plane

Condition for parallel planes

Condition for perpendicular planes

Angle between two planes

Segments on axes

Equation of a plane in segments

Relationship between a plane and a pair of points

Point to plane distance

Polar parameters of the plane

Normal Equation of a Plane

Reducing the plane equation to normal form

Equations of a line in space

Canonical equation of a straight line

Parametric equations of a straight line

Direction vectors

Angles between line and coordinate axes

Angle between two lines

Angle between line and plane

Condition of parallel line and plane

Condition of perpendicularity of a line and a plane

Elementary Geometry, plane:

Triangle area

Median of triangle

Triangle height

Pythagorean theorem

Radius of a circle circumscribing a triangle

Radius of a circle inscribed in a triangle

Area of a parallelogram

Area of a rectangle

Square area

Trapezoid area

Rhombus area

Circle area

Sector area

Length of the arc of a circle

Elementary Geometry, space:

Parallelepiped volume

Cuboid volume

Cube volume

Pyramid lateral surface area

Pyramid total surface area

Pyramid volume

Truncated pyramid lateral surface area

Truncated pyramid total surface area

Truncated pyramid volume

Cylinder lateral surface area

Cylinder total area

Cylinder volume

Cone lateral surface area

Cone total surface area

Cone volume

Sphere surface area

Sphere volume

System of linear equations:

Substitution method

Cramer's method

Invertible matrix method

Algebra:

Quadratic Equations

Biquadratic Equations

Arithmetic progression, sum of the first n members

Arithmetic progression, finding n-th term

Geometric progression, sum

Geometric progression, finding n-th term

Greatest Common Divisor

Least Common Multiple

The application is being actively developed and supplemented with new calculators. Keep for updates!

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