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Definitions for Exam 2

# Definitions for Exam 2 - Definitions 3.1 A matrix is a...

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Definitions 3.1 A matrix is a rectangular array of number called the entries , or elements , of the matrix. If A is an m x n matrix and B is an n x r matrix, then the product C = AB is an m x r matrix. The ( i, j ) entry of the product is computed as follows: (see p. 139) The transpose of an m x n matrix A is the n x m matrix A T obtained by interchanging the rows and columns of A . That is, the i th column of A T is the i th row of A for all i . A square matrix A is symmetric if A T = A – that is, if A is equal to its own transpose. 3.3 If A is an n x n matrix, an inverse of A is an n x n matrix A’ with the property that AA ’ = I and A’A = I Where I = I n is the n x n identity matrix. If such an A’ exists, then A is called invertible . An elementary matrix is any matrix that can be obtained by performing an elementary row operation on an identity matrix. 3.4 Let A be a square matrix. A factorization of A as A = LU, where L is unit lower triangular and U is upper triangular, is called an

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Definitions for Exam 2 - Definitions 3.1 A matrix is a...

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