Sumários

24 Maio 2022, 11:00 • Alexandra Symeonides

Clarifications and examples over different topics of the programme.

19 Maio 2022, 14:30 • Alexandra Symeonides

ex. 21 f) 24 a) 26 b)e) 29 b)e) 31 b)

17 Maio 2022, 10:00 • Alexandra Symeonides

Systems of linear equations (SLEs): firsts definitions and classification. Matricial form

and augmented matrix. Elementary operations and equivalent systems.

Classification of SLEs (number of unknowns vs rank of the matrix of the system and the

augmented matrix). Resolution by Gauss elimination method. Cramer rule for square

Cramer SLEs.

16 Maio 2022, 10:00 • Alexandra Symeonides

Relation between invertibility of a square matrix and rank, inverse matrix by Gauss reduction

method. Properties regarding powers, inverse and transpose of a square matrix.

Determinant of a square matrix of type 2x2. Principal minors.

Recursive definition of the determinant by Laplace’s rule. Determinant of the transpose

and of triangular matrices. Relation between determinant and invertibility. Determinant

of the product; the inverse and integer powers of a matrix.

12 Maio 2022, 14:30 • Alexandra Symeonides

Matrices. exercises 10. (a)(d)(e)(i); 13. (a)(b)(c); 16 (e); 18 (a); 19(a); 20; 23.