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82
Economic Dynamics
per gram. If this charcoal was formed during the reign of Hammurabi,
what is the likely time of Hammurabi’s succession?
9.
(i)
f
1
(
x
) and
f
2
(
x
) are linearly dependent if and only if there exists con
stants
b
1
and
b
2
not all zero such that
b
1
f
1
(
x
)
+
b
2
f
2
(
x
)
=
0
for every
x
. Suppose
b
1
±=
0, then
f
1
(
x
)
=−
(
b
2
/
b
1
)
f
2
(
x
) and so
f
1
(
x
) is a multiple of
f
2
(
x
) and therefore the functions are linearly
dependent. If the set of functions is
not
linearly dependent, then
f
1
(
x
)
and
f
2
(
x
) are linearly independent. Show that
y
1
=
e
rt
and
y
2
=
te
rt
are linearly independent.
(ii)
f
1
(
x
),
f
2
(
x
) and
f
3
(
x
) are linearly dependent if and only if there exist
constants
b
1
,
b
2
and
b
3
not all zero such that
b
1
f
1
(
x
)
+
b
2
f
2
(
x
)
+
b
3
f
3
(
x
)
=
0
for every
x
. If the set of functions is
not
linearly dependent, then
f
1
(
x
),
f
2
(
x
) and
f
3
(
x
) are linearly independent. Show that
y
1
=
e
rt
,
y
2
=
te
rt
and
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This note was uploaded on 12/14/2011 for the course ECO 3023 taught by Professor Dr.gwartney during the Fall '11 term at FSU.
 Fall '11
 Dr.Gwartney
 Economics

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