2270 Chapter 2 Lecture Topics S2019

1. Linear Algebraic Equations
   linearequDRAFT.pdf
   backSubstitutionRemarks2013.txt Why combo is identical to back-substitution.
   jibberish-example.txt Why the lectures use toolkit sequences instead of college algebra methods.
   
2. Matrix Equations, Rank and Nullity
   rankNullityElimination.pdf
   matrixOperations2008.pdf
   matrix-eqn.pdf Fundamental Theorem on Tookit Sequences is Theorem 11, page 326 with proof on page number 334 [19th page] of this reference.
   vec-matrix.pdf
   functionsInfinitelyLongColVector.pdf Cannot understand why functions are vectors? Read this.
3. Orthogonality
   orthogonality.pdf
4. Independence, Pivot Theorem
   independence.pdf
   Pivot Theorem and proof pivotTheorem.pdf
   
5. No Solution Example, using Maple
   exampleNoSolutionChapter3.pdf
   exampleNoSolutionChapter3.mpl
   exampleNoSolutionChapter3.mw
   
6. Linear Transformations, Coordinates
   linearTransformation.pdf
   geometryLinearTransformation.pdf
   
7. Determinants
   determinants2008.pdf
   determinant-theory.pdf
   
8. Inverses of Matrices and Linear Transformations
   inverseMethodRREF.pdf
   elementaryMatricesTheorem.pdf Sildes. Fundamental theorem on toolkit sequences.
   
9. Vector Space Properties
   vectorModelsVectorSpaces.pdf
   
10. Parking Lot Analogy
    Figure: Parking Lot Analogy for Subspace of a Vector Space
    Manuscript: vec-matrix.pdf