## A Course in Linear Algebra with Applications |

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### Contents

Chapter One Matrix Algebra | 1 |

Chapter Two Systems of Linear Equations | 35 |

Chapter Three Determinants | 65 |

Chapter Four Introduction to Vector Spaces | 101 |

Chapter Five Basis and Dimension | 131 |

Chapter Six Linear Transformations | 169 |

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### Common terms and phrases

arbitrary belongs bilinear form characteristic polynomial coefficient matrix column operations column space column vector complex matrix compute coordinate vector corresponding defined denote det(A determinant diagonal entries diagonal matrix diagonalizable dimension eigenvalues eigenvectors elementary matrices elementary row operations elements equals EXAMPLE EXERCISES field F field of scalars finite-dimensional vector spaces finitely generated vector form a basis Hence inner product space integers invertible matrix isomorphic Jordan normal form least squares solution line segments linear algebra linear combination linear differential equations linear operator linear system linear system AX linear transformation linearly independent minimum polynomial null space number of pivots obtain ordered basis orthogonal matrix orthonormal basis permutation plane Proof properties Prove quadratic form real numbers reduced row echelon represented respect row echelon form row space rows and columns scalar multiplication skew-symmetric solve square matrix standard basis subspace Suppose systems of linear THEOREM unique zero vector