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Module Objective: To introduce students to vector spaces, linear transformations , eigenvalues and applications of linear algebra.
Definition of n x n determinant via permutations, determinants of products; inverses of n x n matrix via row reduction, mention adjoint formula and Cramer's rule; coordinate geometry and vectors in n-dimensions; vector spaces; linear span, linear independence, basis and dimension; linear maps and matrices; rank and nullity; rotations, reflections and projections in 3 dimensions; Eigenvalues and eigenvectors of a matrix, diagonalization; symmetric matrices. Applications, for example: computer graphics, Markov processes, principal component analysis. Computation using mathematical computing software.
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