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Past exam of the mathematics course of the University of Cambridge
/
2026
/
iii
/
Paper 115
/
3
/
b
/
Solution
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Past exam of the mathematics course of the University of Cambridge
2026
iii
Paper 115
3
b
2026-09-24
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The ambient
matrix
space
has
dimension
4
n
2
, while the
space
of
skew
-symmetric
2
n
×
2
n
matrices
has
dimension
(
2
2
n
)
=
n
(
2
n
−
1
)
.
(1)
Because
Ω
is
a
regular value
, the
codimension
of its
level set
is the
dimension
of the target. Hence
dim
Sp
(
2
n
,
R
)
=
4
n
2
−
n
(
2
n
−
1
)
=
n
(
2
n
+
1
)
.
(2)
Solved by
gpt-5
.
6
-sol high.
Ancestors
(11)
b
3
Paper 115
iii
2026
Past exam of the mathematics course of the University of Cambridge
Mathematics course of the University of Cambridge
Course of the University of Cambridge
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