Industrial Engineering

-Matrices: Definition of matrix, Types of matrices, matrix equality, Sum and difference of matrices, The product of scaler and matrix and their properties , Transpose of matrix and its properties - Some Special Matrices and Matrix Applications - Elementary row and column operations in matrices, Reduced row–echelon form, Rank of a matrix, The inverse of a square matrix, - Determinants: The determinant of a square matrix, Laplace's expansion, Properties of determinants -Sarrus rule, Additional matrix, Calculation of the inverse of a matrix with the aid of additional matrix - Systems of Linear Equations: Solving systems of linear equations with the aid of equivalent matrices, Linear homogeneous equations, -Cramer's method, The solution with the help of coefficients matrix -Vectors: Vector definition, the sum of vectors, the difference, the analytical expression vectors, scalar product of vectors, properties of the scalar multiplication Scalar product and its features, the mixed multiplication and properties, and properties of double vector product, -Vector spaces: Definition of vector spaces and theorems. Subspaces. Span concept and fundamental theorems. Linear dependence and linear independence of vectors and some theorems about linear dependence and linear independence. -Bases and dimension concepts and fundamental theorems. Definition of coordinates and transition matrices and some theorems. -Eigenvalues and Eigenvectors: The Calculation of Eigenvalues and Eigenvectors of a square matrix, - The calculation of Inverse and power of a square matrix with the help of the Cayley-Hamilton theorem.

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