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18.085 Computational Science and Engineering I
Fall
2008
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�
4
5
18.085
Quiz
2
November
3,
2006
Professor
Strang
Your
PRINTED
name
is:
SOLUTIONS
Grading
1
2
3
4
1)
(25
pts.)
This
network
(square
grid)
has
12
edges
and
9
nodes.
1
2
3
3
/
4
u
2
= 1
3
/
4
1
/
2
6
1
/
2
1
/
2
1
/
4
7
8
9
1
/
4
u
8
= 0
(a)
Do
not
write
the
incidence
matrix
!
Do
not
give
me
a
MATLAB
code
!
Just
tell
me:
(1)
How
many
independent
columns
in
A
?
8
(2)
How
many
independent
solutions
to
A
T
y
=
0 ?
12
−
8 = 4
(3)
What
is
row
5
(coming
from
node
5)
of
A
T
A
?
�
⎦
I
do
want
the
whole
of
row
5.
0
−
1
0
−
1
4
−
1
0
−
1
0
(b)
Suppose
the
node
2
has
voltage
u
2
=
1,
and
node
8
has
voltage
u
8
= 0
(ground).
All
edges
have
the
same
conductance
c
.
On
the
second
picture
write
all
of
the
other
voltages
u
1
to
u
9
.
Check
equation
5
of
A
T
Au
=
0
(at
the
middle
node).
1
1
1
−
−
+ 4
−
1
−
0 = 0
2
2
2
1
2)
(25
pts.)
Suppose
that
square
grid
becomes
a
plane
truss
(usual
pin
joints
at
the
9
H
V
H
V
nodes).
Nodes
2
and
8
now
have
supports
so
u
2
=
u
2
=
u
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- Fall '10
- staff
- Berlin U-Bahn, MIT OpenCourseWare http://ocw.mit.edu, Professor Strang, U1 U2, x− dx dx, U2 U3
-
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