Day 2: Linear Algebra

• I'm going out of town as of 1:00 until Friday morning, so I won't have office hours this afternoon or tomorrow.

• Assignment for next time: Read 1.2; pp. 25-27, problems #1, 4, 8, 11, 16, 20-22, 30, 33

The assignments can be found on the assignments page.

• Matrices
  • spreadsheets
  • images
  • linear transformations, e.g. averages
  • decompositions (statistical techniques)

• section summary

• Linear equations (e.g. the mean)

• Linear systems:
  • A couple of little systems:
    • #1, p. 11
      • How did you do it back in high school?
      • How do we do it here?
        • Eliminate
        • back-substitute
    • some systems are easy...
      • "diagonal"
    • some systems are "silly":
      • inconsistent
      • redundent
  • The geometry of linear systems
    • exactly one solution
    • no solution
    • infinitely many solutions

• Matrices: use your head to eliminate unnecessary stuff (#1, p. 11)
  • coefficient matrix
  • augmented matrix

• Elementary row operations:
  • The point: Replace a system by a system with the same solution set that's easier to solve
  • What's legal?
    • replacement of a row by a sum of the row and multiples of other rows
    • interchange of rows
    • scaling of a row by a nonzero constant

• Existence and Uniqueness
  • Is there at least one solution? (consistent)
  • Is the solution unique?

• Examples:
  • #10, 16, 20, 26, 32