advertisement

ALGEBRA CHAPTER 3 LINEAR SPACES MATH2011/2014 OUTCOMES At the end of this chapter, every student must MATH2011/2014 (1) understand and be able to define the concepts of : linear space, basis, dimension, independence, rank, eigenvalues and eigenvectors, diagonalization, trace and the Cayley-Hamilton theorem. (2) know how to : determine whether or not a given set forms a linear space; find a basis and the dimension of a linear space; determine whether or not given vectors or functions are independent; ascertain the rank of a matrix find eigenvalues and their corresponding eigenvectors; to diagonalize a matrix; apply diagonalization to solve simultaneous linear differential equations in order to determine trajectories; apply the Cayley-Hamilton theorem; work through and understand related problems in prescribed literature; apply the above techniques to problem solving in related engineering courses. A D Love January 2007 Alg3-Outcomes