PGE 310
TEST #1 (Sept 30, 2009)
1.
Short Answer. SHOW ALL WORK (60 points total; 6 pts each except (h))
Consider the following arrays for (a), (b), and (c) only
u=[2 3 2]; v=[ 3 2 0]; A=[1 1; 2 3; 1 3];
B=[ 2 1; 2 3]
(a)
Compute by hand
>> A(:,2)’*u
>> A(:,2)’*u
Let z= A(:,2) =
1
3
3

z’= [1 1 2]
z’*u
is not possible as both are row vectors
(b)
Compute by hand
>> B*B
>> B*B
=
2*2
1*2 2*1
1*3
2*2
3*2 2*1
3*3
+
+
+
+
B*B =
6 5
10 11
(c)
Determine if u and v’ are orthogonal. If they are, make them orthonormal with respect to
the L
2
norm.
u.v’ = 0
Hence they are orthogonal.
2
2
2
1/2
2
2
2
1/2
2
( 1
2
3
....
)
( 2
3
2 )
17
L
norm of u is
u
u
u
=
+
+
=
+ 
+
=
2
2
2
1/2
2
2
2
1/2
2
( 1
2
3
....
)
( 3
2
0 )
13
L
norm of v is
v
v
v
=
+
+
=
+
+
=
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In order to find the orthonormal vector, divide the given vector by its L2 norm
^
2
u
u
L norm of u
=
Thus,
^
[2
3 2]
13
u

=
^
3
1
* 2
17
0
v
=
(d)
Write the MATLAB code that is equivalent to the following :
(
)
100
50
2
2,4,6
1
5
2
j
k
j
k
=
=
+
+
∑ ∑
sum=0;
for j=2:2:100
for k=1:50
sum=sum+(j*j+5*k+2);
end
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 Spring '06
 Klaus
 Linear Algebra, matlab, Englishlanguage films, ﬁnal value, end end

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