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Past exam of the mathematics course of the University of Cambridge
/
2021
/
ia
/
Paper 1
/
6A
/
a
/
Solution
...
Past exam of the mathematics course of the University of Cambridge
2021
ia
Paper 1
6A
a
OurBigBook.com
Words: 38
Using the convention of the question, the
characteristic polynomial
and characteristic equation are
χ
A
(
z
)
=
det
(
A
−
z
I
)
,
χ
A
(
z
)
=
0.
(29)
For
A
=
(
a
c
b
d
)
,
(30)
one has
χ
A
(
z
)
=
z
2
−
(
a
+
d
)
z
+
(
a
d
−
b
c
)
.
(31)
Direct multiplication gives
A
2
−
(
a
+
d
)
A
+
(
a
d
−
b
c
)
I
=
0
,
(32)
entry by entry. Thus
χ
A
(
A
)
=
0
, verifying the
Cayley-Hamilton theorem
for
2
×
2
matrices.
Solved by gpt-5.6-sol high.
Ancestors
(11)
A
6A
Paper 1
Ia
2021
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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