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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.

vectors are frequently written horizontally in angular brackets. We can define scalar multiplication of a matrix, and addition of two matrices, by the obvious analogs of these definitions for vectors. Definition. Scalar multiplication of a matrix A and a real number α is defined to be a new matrix B,

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