Week 1: February 9-13.
Chapter 1.1 Introduction to
linear systems
Key
points: a) General strategy
for solving a simple system
b) Some systems have
a unique solution, some none and some
infinitely many.
c) Intuition:
Guess when are there infinitely many, one or no
solutions for the
cases with more or less or the same number of
equations as unknowns.
d) Don’t belabor the
geometric intuition.
Homework: 6, 10, 20, 26, 32b, 24*, 37*.
Chapter 1.2
Matrices and Gauss-Jordan elimination
Key
points: a)
Introduction to the term ‘matrices, columns, rows, vector,
coefficient matrix,
augmented matrix’. Stress that this is
terminology and notation for now, but as will become clear, these notions
encapsulate the relevant features of a linear system.
b) Gauss-Jordan elimation for solving a linear
system is a
systematic way
to formulate the procedures introduced in 1.1.
c) Introduce dot product as in Exercise 34 and
show how to solve
such a problem
using Gauss-Jordan elimination.
Homework: 10, 12, 30, 32, 40, 29*, 37*
Chapter 1.3
On solutions of linear systems
Key
points: a) Rank of a matrix.
b) When there are ∞, 0 or 1 solution.
c) Vector form, linear combination.
d) Matrices multiplying vectors, matrix form Ax
= b. Compare
definitions in
1.3.6 and 1.3.8. Stress again that this is terminology for now, but as it turns
out, extremely to the point.
e) A(x1+x2) and A·(k x).
d) Adding matrices, multiplying by scalars.
Homework: 4, 14, 24, 36, 50, 25*, 57*.