Linear Algebra

Matrices, Determinants, and Systems of Linear Equations.

Solving systems of linear equations using matrix method.

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

Matrices. Operations with matrices.

Gaussian elimination method for solving systems of linear equations.

Calculation of determinants

Cramer's Rule.

Symmetric, nonsymmetric, orthogonal, and inverse matrices.

Elements of Vector Algebra and Linear Space Theory.

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

Coordinate transformation. Transition matrix.

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

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

Eigenvalues and Eigenvectors of Matrices. Methods for Finding Them.

Double vector product

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

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

Operations with geometric vectors.

Vector and Mixed Product of Vectors.