Day 26: Linear Algebra

Today:

• Announcements:
  • Hand in Chapter 3 homework
  • the second Exam:
    • The Key
    • Curve: add three points to your (raw) score
    • Some stats (after the curve):
      • Maximum: 94.2%
      • Mean: 77.3%
      • Standard Deviation: 12.6%
    • As before, you can get back 20% of the points you missed by stopping by and discussing your exam with me.
  • Some observations:
    • You can't leave a page blank!

    • There was a lot of "linear mythology" going on! I don't want to mock anyone, but it's important for us to seek to tighten up our expressions, so that they make sense, and so that they express what we really want to say. Some examples:
      • 2x2 matrix + matrix = 2x1 vector
      • A vector spans Rⁿ
      • A vector is a subspace....
      • A matrix is a subspace....
      • A matrix is linearly independent....
      • The solution set of Ax=b is a matrix....
      • A transformation T is in Rⁿ
      • A transformation is a matrix....
      • A transformation is a plane....
      • A transformation spans all of Rⁿ....
      • A transformation has only the trivial solution....
      • "The solution set of an invertible matrix A is linearly independent of the columns of A."
      • "the zero vector exists" when you mean "the zero vector is an element of H₁"....
      • "the transformation will make the matrix smaller and lose dimensions"....

• Questions about old stuff?

• Current Business:
  • 4.3: Linearly Independent Sets; Bases
    • section 4.3 highlights (pdf)