This preview shows pages 1–2. Sign up to view the full content.
Math
136
Assignment 9
Due:
Wednesday,
Mar
31st
1.
Calculate the determinant of the following matrices.
a) A
=
[~
~
~1
il
C)C=Hb~cH
1
3
b) B
=
1
1
1
d) D
=
[1
~
i
1 
i
1 5
1
2
3 8
1
2
2
1
1
~
1
+
2i
[
a+ p
2. a) Prove
that det
~
b+q
e
h
c
+
r]
[a
b
C]
[P
f
=
det
d
e
f
+
det
d
k
9
h
k
9
5
2
4
6
o
2
1 1
1
0
q
r]
e
f
.
h
k
[
a
+
P
b
+
q
C
+
r]
b) Use
part a) to express det
d
+
x
e
+
y
f
+
z
as the sum of determinants of
9
h
k
matrices who entries are not sums.
3. n
x
n
matrices
A
and
B
are said to be similar if there exists an invertible matrix
P
such
that
p
1
AP
=
B.
Prove
that if
A
and
B
are similar, then det
A
=
det
b.
[
0
1
31
52]
4. Determine the inverse of
A =
2
6 7
by the cofactor method.
5. Use Cramer's Rule to solve the following systems.
a)
2XI+X2=1
b)
5XI+X2X3=4
3XI
+
7X2
=
2
9XI
+
X2

X3
=
1
Xl 
X2
+
5X3
=
2
6. Let
A
=
[~
!
JJ
f =
[~:]
and
b
=
Hl]
Assuming
that
A
is invertible
use Cramer's Rule to find the value of
X2
in the solution of the equation
Ax
=
b.
7. In each case either prove the statement or give an example showing
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.