The main object of the course is to understand the basic concepts of Linear Algebra and Analytical Geometry. Course Contents included: Vectors in space, coordinates and vector operations, inner product,outer productand mixed product of vectors. Line in space (vector equation, parametric equations, analytic equations), relative positions of lines. Plane in space (vectorequation,parametric equations, analytic equation), relative positions of planes. Matrices,matrix operations, properties of operations and identities, inversematrix.Determinants, properties of determinants, adjoint matrix, calculating the inversematrix using determinants. Linear systems, scaling a matrix withelementaryrow-transformations and solving linear systems using the Gausselimination method, calculating the inverse matrix using the Gauss-Jordan method, solvinglinear systemsusing the Cramer method. Vector spaces, vector subspaces, sum and intersection of subspaces, linear hulls, linear independence and dependence of vectors,basis and dimension, dimensions’ theorem. Inner product spaces, vector norm,Cauchy-Schwarzinequality, parallelogram rule. Gram-Schmidt orthonormalization, unitarymatrices,QR factorization, least squares problem in a linear system, pseudoinverse matrix. Eigenvalues and eigenvectors of matrices, properties of eigenvalues and eigenvectors, characteristic polynomial. Diagonalization of a matrix, Cayley-Hamilton theorem, minimum polynomial. Diagonalization of symmetric real matrices, quadratic forms.