Four Colours vs Linear Algebra Pro

Could be a map of USA or your country colored using four colors in such a way that Nebraska and Missouri (as well as any two contiguous regions or states) wouldn’t be filled with one color? It turns out that you can manage to do it with any map. And this seems to be the first statement in science proved with computer aid. You can verify this statement for variety of maps, study up geography and visit Martin Gardner country by the way. Maps in this release: • Commonwealth of Australia, • Republic of Austria, • French Republic, • Federal Republic of Germany, • United Mexican States, • Republic of Poland, • Portuguese Republic, • Kingdom of Spain, • Kingdom of Sweden, • Swiss Confederation, • United States of America, • United Kingdom of Great Britain and Northern Ireland.

Linear Algebra Pro is a powerful and easy-to-use tool for calculating matrices, determinants, and vector operations — perfect for students, engineers, and anyone who works with linear algebra in study or professional tasks. The app performs step-by-step calculations with detailed solutions using the correct formulas. You can work with matrices up to 5×5 and vectors in 2D or 3D. Each calculator includes a brief theoretical overview to help you understand the concept behind the operation. It also includes a random number generator to instantly create practice problems with random values. Available in 8 languages: English, French, German, Italian, Portuguese, Spanish, Russian, Ukrainian. Whether you're learning, teaching, or solving real-world problems, Linear Algebra Pro helps you get accurate results quickly and understand the math behind them. The application perform following operations with matrices: • Matrix addition • Matrix subtraction • Matrix scalar multiplication • Matrix square • Matrix multiplication • Matrix transposition Determinant calculations: • Calculation of the determinant using the Sarrus method • Calculation of the determinant using the Laplace method Vector operations: • Vector Length • Vector coordinates by two points • Vectors addition • Vectors subtraction • Scalar and vector multiplication • Scalar product of vectors • Cross product of vectors • Mixed (scalar) 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 Download now and simplify your linear algebra work!