## Elementary matrix algebra with linear programming |

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### Contents

I Introductory Concepts | 1 |

2 Matrices with Real Elements | 23 |

3 Systems of Linear Equations and GaussJordan Reduction | 59 |

Copyright | |

8 other sections not shown

### Common terms and phrases

2-space additive inverse algebra arrow augmented matrix basic variables basis matrix called Chapter coefficients cofactors compute Consider the set coordinate matrix corner point corresponding Cramer's Rule defined definition denote determinant diagonal dimension eigenvalue eigenvectors elements Example Exercises extreme points f(xu x2 feasible region Find xu free variables Gauss-Jordan reduction homogeneous increase linear combination linear equations Linear Programming linear transformation linearly dependent set linearly independent LP problem m x n matrix multiplication maximized multiplicative inverse non-basic variables non-negative non-zero obtain ordered pairs original plane polynomial Proof properties quadratic rank reader real numbers satisfy scalar multiplication set of equations set of vectors simplex algorithm slack variable solve spanning set square matrix stochastic matrix submatrix subset subspace Suggested reading Suppose Tableau Theorem unique vector space verify xu x2 zero