Description

Theory
2

Theory/Practice
2

Instructors

Maria da Graça Marcos

Contents

1. Matrices (20%)
Definition and representation. Elementary operations. Basic operations in matrices: sum, product by a scalar, product of matrices, exponentiation. Properties. Inverse matrix. Rank of a matrix.
 

2. Determinants (10%)
Determinant of a matrix: definition, computation and properties.
 

3. Systems of Linear Equations (20%)
Solving systems using Gauss-Jordan method. Cramer System. Cramer´s Rule. Discussion of solutions for different values of the parameters.
 

4. Real Vector Spaces (20%)
Definition and properties. Vector subspaces. Linear combination of vectors; vectors generating a vector space; linearly dependent and independent vectors. Basis and dimension of a vector space.
 

5. Linear Transformations (5% - 10%)
Definition and properties. Kernel and image. Matrix of a linear transformation.
 

6. Analytical Geometry (20% - 25%)
Cross product and dot product of two vectors. Equations of line and plane. Intersections of lines and planes. Relative positions of line and plane. Distan

Learning Outcomes

Students should be able to perform the fundamental operations of matrices, compute determinants and solve matrix equations; apply determinants and matrices in the resolution and discussion of linear equations systems; identifying and generating vector spaces and work with vectors, in particular to check if they can be used as a basis for a vector space; identify linear transformations and matrices associated; give analytical expressions for lines and planes. Study intersections of lines and planes, compute distances, and determine the loci that meet some pre-defined conditions (OB1).
Recognize the importance and apply the different mathematical techniques studied and applied these knowledge to specific problems in their area of Engineering (OB2).