Appendix E  Errata
These errors have been discovered since the second printing in 1996. There is a previous page of errors that
were corrected in the second printing.
Page 18, Exercise D4
The reference to D5 should be to D3.
Page 21
The line after the first equation should read
→
AB
=
b
−
a
.
Page 25
line 1, equivalent.
Page 73, Example 6
left matrix, last row, last entry should be
−
2 (and not 2).
Page 146
second line from the bottom should be
g
(
k
x
)
negationslash
=
kg
(
x
).
Page 185, B2(d)
As defined, the set is empty (no
x
can satisfy the equation), so the set is not a subspace.
This is not what was intended.
Replace (1
,
1
,
1) on the righthand side of the equation by (2
,
3
,
4);
then the set is not empty, but it is not a subspace because is it not closed under the addition or
multiplication by scalars.
Page 207
The discussion of
L
is wrong.
L
is lowertriangular, but it does not have such a simple form.
However, by examining carefully inverses and products of lower triangular elementary matrices (and
the order is very important), we can show that
L

1
=
1
0
0
. . .
0
−
ℓ
12
1
0
. . .
0
.
.
.
.
.
.
.
.
.
.
.
.
−
ℓ
n
1
−
ℓ
n
2
−
ℓ
n
3
. . .
1
,
where the
ℓ
ij
are as described on page 206. Then, in the next paragraph, instead of “
LU
=
A
” we
have
LA
=
U
so
A
=
L

1
U
, and this is the claimed decomposition of
A
into the product of a lower
triangular matrix
L

1
with an upper triangular matrix
U
. The solution procedure described in the
middle of page 207 must be revised to agree with this, and in the matrix at the bottom of page 207,
the below diagonal entries should be
−
ℓ
ij
to agree with the notation on page 206. (In fact, it would
be better to revise the notation on page 206 so that we do get
A
=
LU
; such a revision is presented
starting on page E2.)
This preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
This is the end of the preview.
Sign up
to
access the rest of the document.
 Spring '08
 CELMIN
 Math, Row, Ly, 146 second

Click to edit the document details