Home Work 5
Due May 5, 2008
Three pages
All sections covered in home work assignments (including this one) are included
for the midterm on May 7th.
The best way to prepare is to go through the
problems at the back of each section.
Note
: If you are having difficulties with
these problems make sure you bring them up in your discussion sessions.
1.
(a)
Write the 6x4 incidence matrix A for the graph in Figure 1.
The
y
1
y
2
y
4
y
5
y
6
x
4
x
1
x
2
y
3
x
3
Figure 1: For problem 1.
vector (1,1,1,1) is in the nullspace of A, but now there will be
m

n
+ 1 = 3 independent vectors that satisfy
A
T
y
= 0. Find the three
vectors
y
and connect them to the loops in the graph.
(b)
Write down the dimensions of the four fundamental subspaces for the
incidence matrix A from the previous problem, and a basis for each
subspace.
2.
Every straight line remains straight after a linear transformation. If
z
is
halfway between
x
and
y
, show that
Az
is halfway between
Ax
and
Ay
.
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 Summer '10
 VolkanRodoplu
 Linear Algebra, Vector Space, AZ, linearly independent vectors, independent vectors

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