Finding the Kernel, Nullity, Range, and Rank In Exercises 19-32, define the linear transformation T by T ( x ) = A x . Find (a) k e r ( T ) , (b) n u l l i t y ( T ) , (c) r a n g e ( T ) and (d) r a n k ( T ) . A = [ 0 − 2 3 4 0 11 ]
Finding the Kernel, Nullity, Range, and Rank In Exercises 19-32, define the linear transformation T by T ( x ) = A x . Find (a) k e r ( T ) , (b) n u l l i t y ( T ) , (c) r a n g e ( T ) and (d) r a n k ( T ) . A = [ 0 − 2 3 4 0 11 ]
Solution Summary: The author explains how to find the value kernel of the linear transformation T.
Finding the Kernel, Nullity, Range, and Rank In Exercises 19-32, define the linear transformation T by
T
(
x
)
=
A
x
. Find (a)
k
e
r
(
T
)
, (b)
n
u
l
l
i
t
y
(
T
)
, (c)
r
a
n
g
e
(
T
)
and (d)
r
a
n
k
(
T
)
.
13) Let U = {j, k, l, m, n, o, p} be the universal set. Let V = {m, o,p), W = {l,o, k}, and X = {j,k). List the elements of
the following sets and the cardinal number of each set.
a) W° and n(W)
b) (VUW) and n((V U W)')
c) VUWUX and n(V U W UX)
d) vnWnX and n(V WnX)
9) Use the Venn Diagram given below to determine the number elements in each of the following sets.
a) n(A).
b) n(A° UBC).
U
B
oh
a
k
gy
ท
W
z r
e t
་
C
10) Find n(K) given that n(T) = 7,n(KT) = 5,n(KUT) = 13.
Chapter 6 Solutions
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