Matrices engineering mathematics complete course cover
Matrices is one of the most important and fundamental chapter of engineering mathematics, we have cover complete module for you
Table of Content
1)Types Of Matrix
1.1 -Singular And Non-Singular Matrix.
1.2 -Symmetric And Skew-Symmetric Matrix.
1.3 -Hermitian And Hermitian Matrix.
1.4-Orthogonal MAtrix.
1.5-Unitary Matrix.
2)Rank Of Matrix
2.1 -Echelon Form.
2.2 -Reduction to Normal Form With Sums.
2.3 -PAQ in Normal Form.
3)Linear Dependence and independence of Vector.
4)System of Homogeneous and Non-HomogeneousEquation.
5)Application of Inverse of matrix to coding theory
List of all lecture
theory of Matrices engineering mathematics
In engineering mathematics, a matrix is a rectangular array of numbers or other mathematical objects, such as functions or vectors, arranged in rows and columns. Matrices are widely used in engineering to represent and solve systems of linear equations, to perform operations such as matrix multiplication and inversion, and to model various physical and engineering systems.
Matrices are denoted using capital letters, such as A, B, C, etc., and their entries are denoted using lowercase letters, such as a_ij, b_ij, c_ij, etc. The dimensions of a matrix are given by the number of rows and columns it contains, and are denoted as m x n, where m is the number of rows and n is the number of columns.
Matrices are used in a wide range of engineering applications, including structural analysis, electrical circuit analysis, control systems, and image processing. They are also used in optimization problems, such as linear programming, where the objective function and constraints can be represented as matrices.
One of the most important uses of matrices in engineering is in solving systems of linear equations. A system of linear equations can be represented in matrix form as Ax=b, where A is the coefficient matrix, x is the vector of unknowns, and b is the vector of constants. This system can be solved using various techniques, such as Gaussian elimination or matrix inversion, which are based on matrix operations.
Another important application of matrices in engineering is in the field of control systems, where they are used to model and analyze the behavior of dynamic systems. Matrices are used to represent the state variables of the system, and to describe the system dynamics using differential equations. This enables engineers to design controllers that can manipulate the system state to achieve desired performance objectives.
Overall, matrices are a fundamental tool in engineering mathematics and have a wide range of applications in various fields of engineering.