The student will adquire the basic concepts of 1. Linear systems. 2. Matrix and vector algebra. 3. Linear subspaces in Rn. The student will adquire the following skills 1. To compute the solution of a linear system of equations 2. To decide the uniqueness and existence of the solution of a linear system of equations 3. To work with vectors and matrices 4. To compute the inverse of a matrix 5. To compute bases of linear subespaces 6. To compute eigenvalues and eigenvectors of a matrix 7. To compute an orthonormal basis 8. To solve least square problems 9. To diagonalize symmetric matrices through orthogonal transformations.