3 Hours/Week, 3 Credits

Matrix: definition of a matrix, different types of matrices, addition and multiplication of matrices. Adjoint and inverse of matrix, Cramer’s rule, application of inverse matrix and Cramer’s rule. Elementary row operations and echelon forms of matrices, rank, row rank, column rank of a matrix and their equivalence, use of rank and echelon forms in solving system of homogeneous and nonhomogeneous equations. Vector space and subspace over reals and direct sum, linear combination linear dependence and independence on vectors, basis and dimension of vector space, quotient space and isomorphism theorems, linear transformations, kernel, rank and nullity nonsingular transformations and matrix representation, changes of basis, eigenvector. Eigenvalues, characteristic equations and Cayley-Hamilton theorem. Similar matrices, canonical forms orthogonal and Hermitian matrices, inner product, orthogonal vectors and orthonormal bases, Gram-Schmidt orthogonalization process. Bilinear and quadratic forms. Generalized inverse.