## Linear Algebra: Theory and ApplicationsWard Cheney and David Kincaid have developed Linear Algebra: Theory and Applications, Second Edition, a multi-faceted introductory textbook, which was motivated by their desire for a single text that meets the various requirements for differing courses within linear algebra. For theoretically-oriented students, the text guides them as they devise proofs and deal with abstractions by focusing on a comprehensive blend between theory and applications. For application-oriented science and engineering students, it contains numerous exercises that help them focus on understanding and learning not only vector spaces, matrices, and linear transformations, but uses of software tools available for use in applied linear algebra. Using a flexible design, it is an ideal textbook for instructors who wish to make their own choice regarding what material to emphasis, and to accentuate those choices with homework assignments from a large variety of exercises, both in the text and online. |

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### Contents

Systems of Linear Equations | 1 |

Vector Spaces | 88 |

Matrix Operations | 186 |

Determinants | 243 |

Vector Subspaces | 289 |

Eigensystems | 367 |

InnerProduct Vector Spaces | 404 |

Additional Topics | 458 |

Deductive Reasoning and Proofs | 563 |

Complex Arithmetic | 581 |

AnswersHints for General Exercises | 585 |

607 | |

611 | |

### Common terms and phrases

algorithm applied augmented matrix axioms basis co-domain coefficients column space column vector complex numbers Consider defined definition denoted dependent Det(A determinant diagonal matrix dimension discs eigenvalues eigenvectors elements equation Ax Establish Explain factorization Figure Find ﬁrst form a linearly formula free variable function Gerschgorin given inner-product space integers invertible matrix kernel LetA linear algebra linear combination linear equations linear system linear transformation linearly independent linearly independent set Maple Mathematica mathematical software MATLAB nontrivial nonzero vector null space obtain orthogonal projection orthonormal pivot positions plane problem PROOF properties real numbers reduced echelon form reduced row echelon row echelon form row equivalent row operations row space row-reduction process scalar multiples Section set of vectors solution solve the system span square matrix subspace surjective symmetric system of equations system of linear Theorem tion triangle upper triangular values vector space verify zero