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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-1 with cofactor expansion. |
| 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)