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The sum of a and b denoted by a b is the m n matrix

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Unformatted text preview: matrices used to build models of: —༉  Transportation systems. —༉  Communication networks. —༉  Algorithms based on matrix models will be presented in later chapters. Here we cover the aspect of matrix arithmetic. Matrix Definition: a matrix is a rectangular array of numbers. A matrix with m rows and n columns is called an m × n matrix. —༉  The plural of matrix is matrices. —༉  A matrix with the same number of rows as columns is called square matrix. —༉  Two matrices are equal if they have the same number of rows and the same number of columns and the corresponding entries in every position are equal. 3 × 2 matrix Nota$on —༉  Let m and n be positive integers and let —༉  The ith row of A is the 1 × n matrix [ai1, ai2, …, ain]. The jth column of A is the m × 1 matrix: —༉  The (i , j)th element or entry of A is the element aij. Matrix Addi$on Defintion: let A = [aij] and B = [bij] be m × n matrices. The sum of A and B, denoted by A + B, is the m × n matrix that has aij + bij as its (i , j)th element. In other words, A + B = [aij + bij]. Example: Note that matrices of different sizes can not be added. Matrix Mul$plica$on Definition: let A be an n × k matrix and B be a k × n matrix. The product of A and B, denoted by AB = [cij] , is the m × n matrix where cij = ai1b1j + ai2b2j + … + akjb2j . Example: The product of A and B is undeWined when the number of columns in the 1st matrix is not the same as the number o...
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