Let S be the standard basis on R2 :
1
0
S = , .
0
1
(1)
Suppose that T : R2 R2 is a linear transformation so that if a vector v R2 is
represented in the standard basis as
1
0 x1
v = x1 + x2 = ,
0
1
x2
(2)
S
then T (v) = 2v. In that case, we can
Problems to Explain
Michael Ippolito
Spring 2016
1
Chapter 1
1.20 - Determine whether the following statements are true or false
a. If cfw_1 P (A), then 1 A but cfw_1
/ A.
False, for example if A = cfw_1, cfw_1 then P (A) = cfw_, cfw_1, cfw_1, cfw_1, cfw
Michael Ippolito
April 8, 2016
1
1.56
We mentioned that there are three ways that a collection S of subsets of a
nonempty set A is defined to be a partition of A
Definition 1 The collection S consists of pairwise disjoint nonempty subsets
of A and every e