This course introduces more algebraic methods needed to understand real world questions. It develops fundamental algebraic tools involving direct sum of subspaces, complement of subspace in a vector space and dimension of the sum of two subspaces. Other topics to be covered are one-to one, onto and bijective linear transformations, isomorphism of vector spaces, matrix of a linear transformation relative to a basis, orthogonal transformations, rotations and reflections, real quadratic forms, and positive definite forms.