cruz (fmc326) – HW08 – gilbert – (56540)
1
This printout should have 10 questions.
Multiplechoice questions may continue on
the next column or page – Fnd all choices
before answering.
001
10.0 points
Evaluate the expression
E
= 2
v
v
v
v
4
1
3
−
3
v
v
v
v
−
3
v
v
v
v
4
−
3
1
3
v
v
v
v
.
1.
E
=
−
72
2.
E
=
−
75
correct
3.
E
=
−
73
4.
E
=
−
74
5.
E
=
−
71
Explanation:
±or a 2
×
2 determinant,
v
v
v
v
a b
c d
v
v
v
v
=
ad
−
bc.
Thus
E
= 2
v
v
v
v
4
1
3
−
3
v
v
v
v
−
3
v
v
v
v
4
−
3
1
3
v
v
v
v
= 2(
−
12
−
3)
−
3(12 + 3)
.
Consequently,
E
=
−
75
.
keywords: matrix, determinant
002
10.0 points
The determinant of an
n
×
n
matrix
A
can
be deFned recursively in terms of the deter
minants of (
n
−
1)
×
(
n
−
1) submatrices of
A
.
True or ±alse?
1.
±ALSE
2.
TRUE
correct
Explanation:
The
Minor
M
jk
of an
n
×
n
matrix
A
is the
determinant
M
jk
= det[
A
jk
]
of the (
n
−
1)
×
(
n
−
1) submatrix
A
jk
obtained
by deleting the
j
th
row and
k
th
column from
A
, while the
Cofactor
C
jk
is deFned by
C
jk
= (
−
1)
j
+
k
det[
A
jk
] = (
−
1)
j
+
k
M
jk
.
The determinant of
A
can then be deFned
in terms of Cofactors by expanding either
along a row as in
det[
A
] =
a
j
1
C
j
1
+
a
j
2
C
j
2
+
...
+
a
jn
C
jn
,
or down a column as in
det[
A
] =
a
1
k
C
1
k
+
a
2
k
C
2
k
+
+
a
nk
C
nk
.
Consequently, the statement is
TRUE
.
003
10.0 points
The determinant of a triangular matrix is
always the sum of the entries on the main
diagonal.
True or ±alse?
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 Spring '08
 PAVLOVIC
 Matrices, Det, Howard Staunton

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