Objectives and competences

To know the mathematical and algebraic concepts on which matrix algebra, linear transformations, the theory of determinants and systems of linear equations are based.

At the end of the curricular unit, the student is expected to be able to
- solve any system of linear equations with any number of unknowns and equations;
- calculate vector images through linear transformations.

Teaching Methodologies

Theoretical classes (1.5 h), where fundamental concepts are presented and some application examples are given, accompanied by tutorial classes (1.5 or 3 h), in which students solve exercises related to the CU.

Syllabus

1. Matrix Algebra (MA)
   Matrix definition.
   Matrix addition and multiplication by a scalar. Matrix multiplication. Transposed matrix.
   Inverse matrix and Gaussian elimination method. Properties of the inverse matrix.
   Matrix diagonal, climbing, triangular, symmetric, hemi-symmetric coupled.
    
2. Linear Transformations (LT)
   Kernel and image of a linear transformation.
   Base of a linear space.
   Matrix of a linear transformation.
   Operations with linear transformations.
   Base change. Passage or transition matrix.
   Effect of base change on the matrix of a linear transformation.
    
3. Theory of determinants (Det)
   Permutations.
   Determinants calculation: Sarrus’ rule and Laplace’s theorem.
   Determinant properties.
    
4. Linear equation systems (SEL)
   Deffinition.
   Kronecker’s theorem.
   Solving systems of linear equations based on the Gauss-Jordan method and Cramer's rule.
   Rouché’s theorem.

Applications in different areas of Bioengineering.