Graded Assignment 1: Definitions and Computational Review

Prepare a 15-20 minute presentation on the definitions and computations related to your topic, including examples. Topics will be assigned randomly but you may trade topics.
  • Vector Addition, Scalar Multiplication, Dot Product and the Length of a Vector
  • Matrix Multiplication
  • Matrix Inversion
  • Gaussian Elimination Method
  • Checking if a Set with 2 Operations is a Vector Space
  • Linear Independence, Span, Basis and Dimension
  • Determinants of 2x2 and 3x3 matrices and the expansion method (Laplaces' formula)
  • Eigenvalues and Eigenvectors
  • Equations of Lines and Planes in 3-D

    If more people join the class:
  • Cramer's Rule
  • Subspaces in R2 and R3
  • Orthogonal Matrix
  • Gram-Schmidt process in R2 and R3