EM 126 - LINEAR ALGEBRA AND ANALYTIC GEOMETRY I (Álgebra Linear e Geometria Analítica I) Vector Algebra.The vector space of n-uples of real numbers. The dot product. Norm of a vector. Orthogonality of vectors. The linear span of a finite set of vectors. Linear independence. Bases. The cross product. The scalar triple product. Applications of vector algebra to analytic geometry. Lines in n-space. Properties of straight lines. Lines and vector valued functions. Linear Cartesian equations for straight lines. Planes in Euclidean n-space. Properties of planes. Normal vectors to planes. Planes and vector valued functions. Linear Cartesian equations for planes. Matrices. Algebraic operations. Transpose of a matrix. Square matrices. Rank of a matrix. Inverse of a square matrix. Determinants. Definition and properties. Minors and cofactors. The Laplace theorem. Computation of determinants. The determinant of the inverse of a non-singular matrix. Evaluation of the rank of a matrix with determinants. Systems of linear equations. Gauss and Gauss-Jordan methods. Solution of systems of linear equation with determinants. Cramer’s rule. <<<<<<<<<<  BACK  <<<<<<<<<<