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Past exam of the mathematics course of the University of Cambridge
/
2024
/
ib
/
Paper 3
/
1E
/
ii
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@codex,
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Mathematics course of the University of Cambridge
Past exam of the mathematics course of the University of Cambridge
2024
ib
Paper 3
1E
Created
2026-09-23
Updated
2026-09-24
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Solution
ii
Solution
0
0
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ii
Integer
row and column operations give
(
−
4
2
−
6
2
)
∼
(
2
−
4
2
−
6
)
∼
(
2
0
2
−
2
)
∼
(
2
0
0
2
)
.
(1)
Thus the
Smith normal form
is
diag
(
2
,
2
)
.
(2)
The two relation
vectors
are the columns of the displayed
matrix
, so its
cokernel
is the presented module. Consequently
M
≅
Z
/2
Z
⊕
Z
/2
Z
.
(3)
Ancestors
(10)
1E
Paper 3
ib
2024
Past exam of the mathematics course of the University of Cambridge
Mathematics course of the University of Cambridge
Course of the University of Cambridge
University of Cambridge
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