Vectors and Planes vs Linear Algebra

Vectors and Planes App helps visualize and understand 3D linear and quadric structures and their intersections. List of linear structures and combinations: 1. Two vector combination. 2. Plane. 3. Line and plane combination. 4. Two plane combination. 5. Three plane combination. Current list of quadric structures: 1. Two sphere combination. 2. Standard ellipsoid. 3. Ellipsoid in a form of positive-definite matrix. 4. Standard cone. 5. Cone in a form of indefinite matrix. 6. 1-sheet hyperboloid. 7. 1-sheet hyperboloid in a form of indefinite matrix. 8. 2-sheet hyperboloid. 9. 2-sheet hyperboloid in a form of indefinite matrix. 10. Standard cylinder. 11. Cylinder in a form of positive-semidefinite matrix. 12. Hyperbolic paraboloid. 13. Elliptic paraboloid. Current list of combinations of quadric and linear structures: 1. Matrix ellipsoid and line. 2. Standard ellipsoid and plane. 3. Matrix ellipsoid and plane. 4. Matrix cone and line. 5. Standard cone and plane. 6. 1-sheet hyperboloid in matrix form and line. 7. 2-sheet hyperboloid in matrix form and line. 8. Matrix cylinder and line. 9. Elliptic paraboloid and line. 10. Hyperbolic paraboloid and line. Interactive 3D graphs are provided for all of the above. Step by step calculation algorithms are provided for all intersection point sets. Many of the algorithms are based on Linear Algebra concepts. Those, in turn, are explained in our “Matrix Solver Step by Step” app. Version 10 was completely redesigned. Developers hope to get feedback from users at graphmath@aol.com.

Linear Algebra - Matrix Solver 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 app 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!