Subspaces and Bases
We have seen a number of situations when it is convenient to use a different coordinate
system from the original coordinate system. In this chapter we explore this further and
consider coordinate systems for planes in three dimensions
Math 120 Midterm
10/25/11, 11am 12:15PM
Open book, open notes. No computers or internet enabled devices allowed. Give
complete proofs unless otherwise indicated.
1. (12 points) In this problem, you need not explain your answer.
(a) Let S7 be the permutati
Math 120 Final
12/12/11, 3:30pm 6:30PM
Open book, open notes. No computers or internet enabled devices allowed. This
problem set has two pages. Give complete proofs unless otherwise indicated.
1. Let Z[ 3] R denote the set of real numbers which can be wri
Solutions to Homework #2
Math 120, Autumn 2012
1.4.10 (a) Let
G=
a b
0 c
: a, b, c R, a = 0, c = 0
be the set of upper-triangular invertible 2x2 matrices. Want to
check that G is closed under multiplication. We have
a1 b1
0 c1
a2 b2
0 c2
=
a1 a2 a1 b2 + b