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Numerical Linear Algebra with Applications by William Ford

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Chapter 1

Matrices

Abstract

The chapter introduces the concept of vectors and matrices, for which there are many applications in engineering and science. Matrix operations, including matrix multiplication, are introduced, and how to execute these operations using MATLAB is discussed. A system of equations can be expressed elegantly using a coefficient matrix and column vectors. The chapter presents the concept of a linear transformation using rotation and translation matrices. Matrix powers are discussed and applied to a problem in graph theory. The chapter introduces the matrix inverse and some of its properties. In particular, it is shown that a linear system has a unique solution if its coefficient matrix has an inverse. The chapter concludes ...

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