May 2024
Intermediate to advanced
687 pages
18h 35m
English
Content preview from Discrete Mathematical Structures by Pearson
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Author: Uma Shanker Gupta and ISBN: 978-93-325-2139-1
Solution Manual A-103
And
|| ||
,s
ivv
vx
dx
2
2
22
2
∼∼∼
=< >=
−
∫
1
n
p
p
p
==
−
∫∫
1
2
1
12
2
00
pp
pp
(sin )(cos)xd
xx
dx
=−
==
12
2
1
1
0
pp
p
p
x
xsin
.
23. Let f (t) = sin pt, g(t) = sin qt
<>=
−
∫
fg pt qt dx
,sin sin
p
p
=
1
−− +
−
∫
2
[cos()cos( )]pqtpqtdt
p
p
=
1−
−
−
+
+
=
−
2
0
sin( )sin()
,
pqt
pq
pqt
pq
p
p
when p ≠ q
Hence, the functions are orthogonal.
Also || || ,sin sinfffptd
tp
tdt
222
0
2=< >= =
∫∫
−
p
p
p
=−
∫
(cos )12
0
pt dt
p
=−
=t
pt
p
sin2
2
0
p
p
∴=
|| ||f
p
Therefore the orthonormal set is
11
2
1
pp p
sin, sin,..., sintt nt
24. The given vectors are
xx x
12 3
110 101 234
==−=
(,,),(,,), (,
,)
Applying ...
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