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Past exam of the mathematics course of the University of Cambridge
/
2025
/
ii
/
Paper 4
/
19J
/
b
/
i
/
Solution
...
2025
ii
Paper 4
19J
b
i
OurBigBook.com
Words: 31
Write
u
(
x
)
=
(
1
0
x
1
)
.
(218)
Since
u
(
x
)
u
(
y
)
=
u
(
x
+
y
)
,
χ
(
v
⋅
)
(
u
(
x
+
y
))
=
χ
(
u
(
vx
+
v
y
))
=
χ
(
u
(
vx
))
χ
(
u
(
v
y
))
=
χ
(
v
⋅
)
(
u
(
x
))
χ
(
v
⋅
)
(
u
(
y
))
.
(219)
Thus
χ
(
v
⋅
)
is a one-dimensional representation of
U
; for
v
=
0
it is the trivial representation.
Solved by gpt-5.6-sol high.
Ancestors
(12)
I
B
19J
Paper 4
Ii
2025
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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