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Matrices, System of Linear Equations, Gauss Elimination Method
n linear algebra, Gaussian elimination (also known as row reduction) is an algorithm for solving systems of linear equations. It is usually understood as a sequence of operations performed on the corresponding matrix of coefficients.
Amrendra Pratap
Determinant and its properties
Properties of determinants Interchange two rows or cols changes the sign: -> -1 * det(A) ... transpose -> det (A) unchanged. ... multiply row * k -> k * det(A) ... multiply matrix * k -> k^2 * det(A) ... det (A B) -> det(A) * det(B) ... proportional rows or columns -> det() == 0. ... Add multiple of one row to another -> det unchanged. ... Geometric interpretation.
Introduction to ode, Concept of Solutions, Applications
In mathematics, an ordinary differential equation (ODE) is a differential equation containing one or more functions of one independent variable and its derivatives. The term ordinary is used in contrast with the term partial differential equation which may be with respect to more than one independent variable
Solution of First Order Equations
First-Order Linear Differential Equations: A First order linear differential equation is an equation of the form y + P(x)y = Q(x). ... We can solve this equation in general but it is better to understand how to solve it than it is to just memorize the solution.
Stress due to bending
Normal Stress in Bending. ... Bending results from a couple, or a bending moment M, that is applied. Just like torsion, in pure bending there is an axis within the material where the stress and strain are zero. This is referred to as the neutral axis.
Echelon Form, Elementary Matrices & Row Reduction
Elementary Operations. There are three kinds of elementary matrix operations. Multiply each element in a row (or column) by a non-zero number. Multiply a row (or column) by a non-zero number and add the result to another row (or column).
Dimension of Vector Space
Image result for : Dimension of Vector Spacemath.stackexchange.com In mathematics, the dimension of a vector space V is the cardinality (i.e. the number of vectors) of a basis of V over its base field. It is sometimes called Hamel dimension (after Georg Hamel) or algebraic dimension to distinguish it from other types of dimension.
Linear Transformation & Rank-Nullity Theorem
Image result for Linear Transformation & Rank-Nullity The rank-nullity theorem is a fundamental theorem in linear algebra which relates the dimensions of a linear map's kernel and image with the dimension of its domain.