Day 2: Linear Algebra

• Announcements:
  • The problem assignments can be found on the assignments page. If we are discussing section X on a given day, then I will have expected you to have read section X - okay?

  • Another Motivation for linear algebra: find your love! eHarmony has its 29 dimensions:
    "eHarmony is the only relationship site on the web that creates compatible matches based on 29 dimensions scientifically proven to predict happier, healthier relationships."

• Today we take a look at Section One.I.1: Linear systems.Solving Linear Systems.Gauss's Method
  • The chapter begins with two examples from the sciences: physics and chemistry. I'll throw in another example -- buying a car.

  • The solution method in each case of a linear system is the same: Gaussian elimination

  • There are three operations that we use to reduce a system where it can be solved by back-substitution.
    • Swapping distinct rows
    • Scaling rows by a non-zero constant
    • Combining distinct rows

  • These "row operations" preserve the solution set: that is, they preserve solutions of the original linear system, and do not introduce any new, spurious solutions.

  • As we discussed last time, there are three things that might happen: a linear system may have either
    • a unique solution;
    • no solution;
    • infinitely many solutions.

  • Examples:
    2. 1.18(b*) -- close to 1.18(b)!
    4. 1.18(f)

Links:

• Octaveweb