## 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 | |

15 other sections not shown

### Common terms and phrases

_ X2 a1nXn Abelian Groups angle axis coefficients column rank column-vectors consider contains cos2 deduce defined definition direction-cosines direction-ratios echelon form echelon matrix elementary matrices elements endpoints equations X1 Example EXERCISES formula geometrical gives half-line Hence homogeneous equations hu h2 independent vectors inner product intersection inverse L. E. DICKSON L{Xi line joining linear algebra linear equations linear mapping linearly dependent localized vectors m x n midpoints n x n matrix non-trivial solution non-zero null space obtain operations original orthogonal parallel perpendicular plane point H Proof prove Theorem ratio rational canonical form real numbers regular matrices row rank row-equivalent row-vectors satisfies the equation set of equations set of vectors Show Solve the equations submatrix symmetrical form Theorem Theory three dimensions three vectors trivial solution unique unity matrix vector space vector subspace vectors X1 Vn(R write Xr+1 Xu X2 zero vector