TEST #1 (Sept 30, 2009)
PGE 310
1.
Short Answer. SHOW ALL WORK (60 points; 6 pts each except (h))
Consider the following arrays for (a), (b), and (c) only
u=[1 2 1]; v=[ 3 1 1]; A=[2 1; 3 1; 2 2];
B=[ 1 2; 3 1]
(a)
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 ....
)
(1
2
1 )
6
L norm of u is
u
u
u
=
+
+
=
+ 
+
=
2
2
2
1/2
2
2
2
1/2
2
( 1
2
3 ....
)
( 3
1
1 )
11
L norm of v is
v
v
v
=
+
+
=
+
+ 
=
In order to find the orthonormal vector, divide the given vector by its L2 norm
^
2
u
u
L norm of u
=
Thus,
^
[1 2 1]
6
u

=
^
3
1
* 1
11
1
v
=

(b)
Compute by hand
>> A(:,2)’*u
Let z= A(:,2) =
1
1
2
z’= [1 1 2]
z’*u
is not possible as both are row vectors
(c)
Compute by hand
>> B*B
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1*1 3*2 1*2 2*1
3*1 3*1 3*2 1*1
+
+
+
+
B*B =
7 4
6 7
(d)
The pressure in a system is a function of both temperature and concentration. It is governed
by the following equation.
( )
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 Spring '06
 Klaus
 Linear Algebra, matlab, Englishlanguage films, ﬁnal value, end end

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