## A Geometric Introduction to Linear Algebra |

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### Contents

Chapter One Coordinate Geometry of the Plane | 1 |

Chapter Two Vectors in Two Dimensions | 21 |

Chapter Three Coordinate Geometry of Three Dimensions | 38 |

Copyright | |

12 other sections not shown

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### Common terms and phrases

_ X2 a1nXn angle arXr axis coefficients column-vectors consider contains cos2 Cramer's rule deduce defined definition direction-cosines direction-ratios echelon form echelon matrix elementary matrices elements endpoint equations X1 Example EXERCISES formula geometrical gives half-line Hence homogeneous equations independent vectors inner product intersection inverse inverse matrix L{XX L{YX line HK line joining linear algebra linear equations linear mapping linearly dependent localized vectors midpoints n-dimensional vectors non-trivial solution non-zero null space obtain operations origin orthogonal parallel perpendicular plane point H postmultiplication premultiplication Proof prove Theorem ratio rational canonical form real numbers regular matrices respectively row rank row-equivalent row-vectors satisfies the equation scalar multiplication set of equations set of vectors Show Solve the equations submatrix symmetrical form Theorem three dimensions three vectors trivial solution unique unity matrix vector space vector subspace vectors Xx Vn(R write Xr+1 zero vector