Linear Algebra

Matrices, Determinants, and Systems of Linear Equations.

Solving systems of linear equations using matrix method.

Gaussian elimination method for solving systems of linear equations.

Elementary transformations. Matrix rank. Solving homogeneous systems of equations.

Matrices. Operations with matrices.

Calculation of determinants

Symmetric, nonsymmetric, orthogonal, and inverse matrices.

Cramer's Rule.

Elements of Vector Algebra and Linear Space Theory.

Linear combinations, linear dependence of vectors. Collinear and coplanar vectors.

Scalar product of vectors, properties. Length of vectors. Angle between vectors.

Projections of a vector. Direction cosines. Cauchy-Schwarz inequality.

Basis of a linear space. Decomposition of a vector by basis.

Coordinate transformation. Transition matrix.

Eigenvalues and Eigenvectors of Matrices. Methods for Finding Them.

Double vector product

Polar, cylindrical, and spherical coordinate systems. Transition formulas.

Vector and Mixed Product of Vectors.

Operations with geometric vectors.