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multiplication by scalars). Transposition. Identity, diagonal and symmetric matrices.

4. DETERMINANTS. Defmition - Laplace expansion. Cofactor of an element of matrix. Determinant of transposed matrix. Elementary transformations of a determinant. Cauchy theorem. Nonsingular matrix, inverse matrix. Computation of inverse matrix by cofactors.

2

5. SYSTEMS OF LINEAR EQUATIONS. Cramer theorem. Homogeneous and nonhomogeneous systems. Solving of arbitrary Systems of linear equations. Gauss elimination - transformation to upper triangular matrix. The case of nonsingular triangular matrix.

2

6. ANALYTIC GEOMETRY IN SPACE. Coordinate system. Operations on vectors in R3. Length and scalar product of vectors. Angle between vectors. Cross product and triple product of vectors - computing area and volume. Piane. Equations of a piane. Normal vector of a piane. Angle between planes. Mutual location of planes. Linę in space. Linę as intersection of two planes. Equations of a linę. Mutual location of two lines. Distance between a point and a piane or a linę.

3

7. COMPLEX NUMBERS. Operations on complex numbers in algebraic form. Conjugate numbers. Modulus. Polar form of complex number. Principal argument. De Moivre formula, n-th roots of a complex number.

3

8. POLYNOMIALS. Operations on polynomials. Root of polynomial. Bezout theorem. Fundamental theorem of algebra. Decomposition of a plynomial into factors. Decomposition of rational function into a sum of simple real fractions.

2

Contents of particular hours

Number of hours

1. Exercises illustrating the materiał presented during the lectures.

18