- Last Time: Echelon forms
- Announcements:
- Assignment for next time: work on your problems, and come
with questions. Remember that your assignments will be due on Friday, 9/3: I'll
probably just roll the die to decide which of the three I'll pick up: this will
produce essentially the same number of assignments collected as would randomly
choosing to grade each with 1/3 probability (the expected values of the number
of assignments is the same).
- Today:
- Last time: Gaussian elimination:
reducing matrices to row echelon form
- Problems from last time:
- #7, p. 25 (what's the geometry like?)
- parameterized solutions
- basic and free variables
- #15, p. 25
- #29, 31, p. 26
- New today: Vector
equations
- From calculus class, you are already familiar with vectors in 2-
and 3-space. We want to extend the notions you've already developed into
n-space.
- New idea: span of a set S of vectors: the subspace
of Rn generated by linear combinations of vectors from
S
- You know that the sum of two vectors u and v
is the diagonal vector of the parallelogram generated
by the two vectors.
- Given an arbitrary vector, can you write it as a linear
combination of vectors in the set S?
- Problems, pp. 37-40:
- Next time: Problem session!
Website maintained by Andy Long.
Comments appreciated.
