The exams will cover the following topics:

  1. Can you even RREF?
    • reduced echelon form
    • elementary operations
  2. Vector / Matrix Algebra
    • Matrix-Matrix multiplication
    • Matrix - vector multiplication
    • Dot product
    • vector matrix addition
    • consine law
    • orthogonality
    • length of a vector
    • scalar multiplication
    • matrix transpose
  • Basic solutions of homogeneous systems:
    • span
    • linear independence
    • bases
    • shrinking
    • dimension
    • subspaces
    • Back substitution
    • First/lead varaibles
    • Linear combination
    • superposiiton principle
    • consistent/inconsistent
    • trivial solution
    • impossible/redundant equations
    • matrix notation
    • particular and homogeneous

  1. Systems of linear equations
    • basic solutions
    • consistent/inconsistent
    • particular + homogeneous
    • free/lead variables
    • back substitution
    • matrix notation
  2. Span
    • span
    • linear combinations
    • subspaces
  3. Linear Independence
    • linear independence
    • bases
    • dimension
    • shrinking