## Mathematics for High School: Introduction to Matrix Algebra. Teacher's Commentary, Volume 16 |

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### Contents

THE ALGEBRA OF 2 x 2 MATRICES | 35 |

MATRICES AND LINEAR SYSTEMS | 69 |

REPRESENTATION OF COLUMN MATRICES AS GEOMETRIC VECTORS | 107 |

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2x2 matrices 9 cos a b c d additive inverse additive subset algebra analytic geometry associative associative law axis basis vectors Brand II Brand Chapter characteristic equation characteristic vector Claremore closed under multiplication cofactor collinear column vectors commutative commutative law completes the proof complex numbers concept Connecticut cos 9 cos a sin definition diagonalization method direction cosines distributive law element elementary matrices Elementary Row Operations entries equal equation equivalent example Exercises follows geometric hat trick Hence High School Hunter College identity element identity matrix IIVII inner product integers inverse element isomorphism kernel law of cosines line segment line y linear combination linear equations linear programming linear systems linear transformation linearly independent Lyons Township maps mathematical maturity mathematicians mathematics matrix addition matrix algebra matrix factors matrix inverse matrix multiplication method multiplication table multiplicative inverse multiplicative subset North Haven number system one—to-one onto operations ordered pair orthogonal parallelogram plane plane geometry problem properties quadratic equation quaternions real number system real numbers rotation row vector scalar scalar multiples scalar product second row simultaneous equations sin 9 sin a cos solution square matrix subspace Taft School Theorem Thus Trier Township trigonometry unit vectors University of Oklahoma University of Washington vector addition vector space Vitamin D West Hempstead William Penn Williams College x axis x+y+u+v Yale University York University zero matrix zero vector