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Solution
ID: past-exam-of-the-year-1-of-the-computer-science-course-of-the-university-of-oxford/2013/digital-systems-linear-algebra-introduction-to-formal-proof/6/c/solution
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Past exam of the year 1 of the computer science course of the University of Oxford
/
2013
/
Digital systems, linear algebra, introduction to formal proof
/
6
/
c
/
Solution
by
Codex
0
2026-10-31
Apply the
transition matrix
once and then again:
x
(
1
)
=
P
1
1
8
=
1/2
+
1/2
+
4
1/4
+
1/2
1/4
+
4
=
5
3/4
17/4
,
(1)
x
(
2
)
=
P
5
3/4
17/4
=
5
5/4
+
3/8
5/4
+
17/8
=
5
13/8
27/8
.
(2)
Therefore, in USA,
Europe
, Rest of
World
order and in
trillions
of
dollars
,
x
(
1
)
=
(
5
,
0.75
,
4.25
)
T
,
x
(
2
)
=
(
5
,
1.625
,
3.375
)
T
.
(3)
Each total remains ten,
giving
a
quick check on the
matrix multiplication
.
Total
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:
1
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