Linear Algebra MathRoom |

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Linear Algebra Lessons | ||

logID |
file name |
topics covered |

MATRICES, MATRIX OPERATIONS | ||

lnalg1 | row reducing, elimination | Gaussian elimination, solving systems with row-reduction |

lnalg1.2 | homogeneous systems | solving systems with all constants = 0 |

lnalg1.2a | matrices: operations & properties | operations on matrices, matrix multiplication |

lnalg1.3 | elementary, identity, inverse matrices | inverse, elementary & identity matrices |

lnalg1.4 | determinants, Cramer's rule | determinant properties, theorems, Cramer's rule |

lnalg1.5 | Inverse Matrix with Cofactors | Finding A with cofactor expansion.^{-1} |

VECTORS | ||

lnalg2.0 | vectors in the Cartesian Plane | first lesson on vectors, angles, direction |

lnalg2 | all about vectors | vectors, dot & cross product, norm, geometry |

lnalg2.1 | orthogonal projections | decomposing vectors to orthogonal components |

lnalg3 | lines and planes in 3-space, | equations of lines & planes in R³ |

lnalg3.1 | spheres and tangent planes | equations of spheres and tangent planes in R³. |

VECTOR SPACES: BASIS & DIMENSION | ||

lnalg4.0 | Vector Spaces, Subspaces | defining axioms for vector spaces, subspaces. |

lnalg4 | finding a nullspace basis | finding basis for the nullspace of a matrix A. |

lnalg4.1 | spanning, linear independence, basis | definitions, theorems on vector spaces |

lnalg4.2 | row & column space of a matrix | finding bases for row and column spaces of matrix A. |

lnalg4.3 | mini-series theorem | |

Exercises & Assignments | ||

logID |
file name |
questions on |

vectrsexer | vectors exercise | dot, cross product, norm, orthogonality, projections |

elemtrxexer | elementary matrices exercise | elementary matrices, finding inverse matrix |

elemex-2 | elementary matrices exercise | describing the row operation of an elementary matrix. |

lnalgxr1 | assignment # 1 | matrix arithmetic, solving systems with elimination |

lnalxr2 | assignment # 2 | Solving Systems, Cramer's Rule |

lnalgxr3 | assignment # 3 | vectors, lines and planes in R³ |

lnalgxr3sl | solutions assignment # 3 | solutions for assignment 3 |

lnalgxr4 | assignment # 4 | vectors spaces, sub-spaces, linear combinations |

lnalgxr5 | assignment # 5 | basis, linear independence, spanning |

Tests & Exams | ||

lnalgtst1 | Test # 1 | homogeneous systems, elementary matrices, inverse |

lnalgtst1sl | Test # 1 solutions | solutions for questions in test #1 |

lnalgtst2 | Test # 2 | vectors, determinants, inverses, lines & planes |

lnalgtst2sl | Test # 2 solutions | solutions for questions in test #2 |

lnalgtst3 | Test # 3 | vector spaces, row, column and solution spaces |

lnalgtst3sl | Test # 3 solutions | solutions for questions in test #3 |

lnalgfnl | Final Exam on entire course | matrices, systems, vectors, vector spaces etc. |

lnalgfnlsl | Solutions for Final Exam | solutions for questions on entire course |

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*(all content of the MathRoom Lessons **© Tammy the Tutor; 2002 - 2005)*