Pure Mathematics
... Let be a subgroup of a group . Prove that the normalizer of in (i.e. ) is a subgroup of . Prove that a group of prime order is cyclic. ...
... Let be a subgroup of a group . Prove that the normalizer of in (i.e. ) is a subgroup of . Prove that a group of prime order is cyclic. ...
Muthuvel
... equations by graphing, substitution, elimination by addition, Gauss-Jordan elimination and use of matrix inverse. The systems of equations considered will have a unique solution, no solution or an infinite number of solutions. • Linear Programming: Systems of linear inequalities in two variables, g ...
... equations by graphing, substitution, elimination by addition, Gauss-Jordan elimination and use of matrix inverse. The systems of equations considered will have a unique solution, no solution or an infinite number of solutions. • Linear Programming: Systems of linear inequalities in two variables, g ...
Numerical Solutions of a System of Equations
... where aij , bi , i, j = 1..n are real constants and the a0 s are the coefficients of the variables xi . The above system can be written as AX = b, where ...
... where aij , bi , i, j = 1..n are real constants and the a0 s are the coefficients of the variables xi . The above system can be written as AX = b, where ...
4.3 COORDINATES IN A LINEAR SPACE By introducing
... By introducing coordinates, we can transform any n-dimensional linear space into Rn 4.3.1 Coordinates in a linear space Consider a linear space V with a basis B consisting of f1, f2, ...fn. Then any element f of V can be written uniquely as f = c1f1 + c2f2 + · · · + cnfn, for some scalars c1, c2, .. ...
... By introducing coordinates, we can transform any n-dimensional linear space into Rn 4.3.1 Coordinates in a linear space Consider a linear space V with a basis B consisting of f1, f2, ...fn. Then any element f of V can be written uniquely as f = c1f1 + c2f2 + · · · + cnfn, for some scalars c1, c2, .. ...
Linear algebra
Linear algebra is the branch of mathematics concerning vector spaces and linear mappings between such spaces. It includes the study of lines, planes, and subspaces, but is also concerned with properties common to all vector spaces.The set of points with coordinates that satisfy a linear equation forms a hyperplane in an n-dimensional space. The conditions under which a set of n hyperplanes intersect in a single point is an important focus of study in linear algebra. Such an investigation is initially motivated by a system of linear equations containing several unknowns. Such equations are naturally represented using the formalism of matrices and vectors.Linear algebra is central to both pure and applied mathematics. For instance, abstract algebra arises by relaxing the axioms of a vector space, leading to a number of generalizations. Functional analysis studies the infinite-dimensional version of the theory of vector spaces. Combined with calculus, linear algebra facilitates the solution of linear systems of differential equations.Techniques from linear algebra are also used in analytic geometry, engineering, physics, natural sciences, computer science, computer animation, and the social sciences (particularly in economics). Because linear algebra is such a well-developed theory, nonlinear mathematical models are sometimes approximated by linear models.