Linear Algebra MathRoom

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Linear Algebra Lessons
logID file name topics covered
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.
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.
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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