Transcription of Vectors and Matrices A - MIT
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Vectors and Matrices A - MIT
Vectors and Matrices Appendix A. Vectors and Matrices are notational conveniences for dealing with systems of linear equations and inequalities. In particular, they are useful for compactly representing and discussing the linear programming problem: n X. Maximize cjxj, j=1. subject to: n X. ai j x j = bi (i = 1, 2, .. , m), j=1. xj 0 ( j = 1, 2, .. , n). This appendix reviews several properties of Vectors and Matrices that are especially relevant to this problem. We should note, however, that the material contained here is more technical than is required for understanding the rest of this book. It is included for completeness rather than for background. Vectors . We begin by defining Vectors , relations among Vectors , and elementary vector operations.
A is called square if m = n. The numbers aij are referred to as the elements of A. ... Scalar multiplication of a matrix A and a real number α is defined to be a new matrix B, written B = αA or B = Aα, whose elements bij are given by bij = αaij. For example, 3 1 2 0 −3 = 3 6
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