| Expected results from this subject |
Training and Learning Results |
| RA1. To know how to use gaussian elimination to find an echelon form and the reduced echelon form of a matrix.
|
A2
|
B8
|
C1
C3
C12
|
D4
D6
D11
|
| RA2. To understand and to know how to solve the questions of existence, uniqueness and universal existence for the systems of linear equations. |
A2
|
B8
|
C1
|
D4
D6
D11
|
| RA3. To understand the matrix product and its relationship with the composition of linear maps as well as to know its algebraic properties and its applications. |
A2
|
B8
|
C1
|
D4
D6
D11
|
| RA4. To understand what means for a matrix to have a right inverse, a left inverse or being invertible. |
A2
|
B8
|
C1
|
D4
D6
D11
|
| RA5. To know how to operate with block matrices and to know its properties and applications. |
A3
|
B8
B9
|
C1
C3
|
D4
D6
D7
D11
|
| RA6. To understand the concept of determinant of a square matrix, its properties and how to use those properties to calculate a determinant. To know how to calculate a determinant by the method of cofactors. |
A2
|
B8
|
C1
|
D4
D6
D11
|
| RA7. To understand the concept of vector space and that of linear map as well as the relationship between the concepts of kernel and image of a linear map and those of null space and column space of a matrix. |
A2
|
B8
|
C1
|
D4
D6
D11
|
| RA8. To understand the relationship between the questions of universal existence and uniqueness of solutions of a system of linear equations and the questions of subspace generated by and linear independence of the columns of a matrix, as well as the relationship between those and the properties of surjectivity and inyectivity of a linear map. |
A2
|
B8
|
C1
|
D4
D6
D11
|
| RA9. To find a basis of the null space / column space of a matrix or of the kernel / image space of a linear map. |
A2
|
B8
|
C1
|
D4
D6
D11
|
| RA10. To find the cartesian equations of a subspace determined by means of generators and to find a basis and the cartesian equations of the sum or intersection of two subspaces of R^n. |
A2
|
B8
|
C1
|
D4
D6
D11
|
| RA11. To find the coordinates of a vector with respect to a given basis and to find the change of coordinates matrix from a given basis to another one. |
A2
|
B8
|
C1
|
D4
D6
D11
|
| RA12. To know how to use coordinates to translate problems in abstract vector spaces to problems in R^n. |
A2
|
B8
|
C1
|
D4
D6
D11
|
| RA13. To find the matrix of an endomorphism of a vector space relative to a given basis and to know how to determine the effect of a change of basis on the matrix of the endomorphism. |
A2
|
B8
|
C1
|
D4
D6
D11
|
| RA14. To understand the concept of diagonalization of a square matrix and its application to the calculation of powers of a square matrix and, in general, to the evaluation of a polynomial function on a square matrix. |
A2
|
B8
|
C1
|
D4
D6
D11
|
| RA15. To understand the concept of eigenvector and eigenvalue of a square matrix. |
A2
|
B8
|
C1
|
D4
D6
D11
|
| RA16. To know how to find the characteristic polynomial of a square matrix, its relationship with the eigenvalues and the spectrum of the matrix and the concept of algebraic multiplicity of the eigenvalues. |
A2
|
B8
|
C1
|
D4
D6
D11
|
| RA17. To know how to find a basis of the eigenspace of an eigenvalue of a square matrix and to know how to find a diagonalization of a matrix whose eigenvalues are known. |
A2
|
B8
|
C1
|
D4
D6
D11
|
| RA18. To understand the concepts of scalar product and orthogonality in R^n and to understand the null space of a matrix as the orthogonal space to the row space of the matrix. |
A2
|
B8
|
C1
|
D4
D6
D11
|
| RA19. To calculate the orthogonal projection of a vector on the ray of a nonzero vector and to know how to use such projections to orthogonalize a basis of a subspace of R^n by the Gram-Schmidt algorithm. |
A2
|
B8
|
C1
C12
|
D4
D6
D11
|
| RA20. To understand the problem of least squares associated with an inconsistent system of linear equations and to solve it by means of the corresponding normal equations. |
A2
|
B8
|
C1
|
D4
D6
D11
|
| RA21. To know the orthogonality properties of the eigenspaces of a symmetric matrix and to know how to use them to find an orthogonal diagonalization of a symmetric matrix. |
A2
|
B8
|
C1
|
D4
D6
D11
|
| RA22. To understand the concept of quadratic form and to know how to represent it by means of a symmetric matrix. |
A2
|
B8
|
C1
|
D4
D6
D11
|
| RA23. To understand the concept of change of variable for a quadratic form and to know how to find its effect on the corresponding symmetric matrix. |
A2
|
B8
|
C1
|
D4
D6
D11
|
| RA24. To know how to find a diagonalization of a quadratic form and to know how to use it to classify it and to determine its maximum an minimum values on unit vectors. |
A2
|
B8
|
C1
|
D4
D5
D6
D11
|
