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Solutions to even numbered problems from section 1.6
4a. Suppose an economy has four sectors, Agriculture (A), Energy (E),
Manufacturing (M), And Transportation (T). Sector A sells 10% of its
output to E and 25% to M and retains the rest. Sector E sells 30% of
its output to A, 35% to M, and 25% to T and retains the rest. Sector
M sells 30% of its output to A, 15% to E, and 40% to T and retains the
rest. Sector T sells 20% of its output to A, 10% to E, and 30% to M,
and retains the rest. Construct the exchange table for this economy.
Solution:
A
E
M
T
output
↓
↓
↓
↓
.65
.30
.30
.20
→
A
.10
.10
.15
.10
→
E
.25
.35
.15
.30
→
M
0
.25
.40
.40
→
T
input
8. Balance the chemical equation
KMnO
4
+
MnSO
4
+
H
2
O
→
MnO
2
+
K
2
SO
4
+
H
2
SO
4
Solution:
We will use vectors in
R
5
to list the numbers of “atoms per
molecule” using the following convention:
K
→
Mn
→
O
→
S
→
H
→
⋆
⋆
⋆
⋆
⋆
KM
n
O
4
:
1
1
4
0
0
,
MnSO
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 Fall '08
 AXENOVICH

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