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JEE Main Math Class 12 Matrices Part 2 Questions
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© examsnet.com
Question : 4
Total: 35
Let
A
be a
2
×
2
symmetric matrix such that
A
[
1
1
]
=
[
3
7
]
and the determinant of
A
be 1 . If
A
−
1
=
α
A
+
β
I
, where
I
is an identity matrix of order
2
×
2
, then
α
+
β
equals .....
[4 Apr 2024 Shift 2]
Your Answer:
Validate
Solution:
👈: Video Solution
Let
A
=
[
a
b
b
d
]
[
a
b
b
d
]
[
1
1
]
=
[
3
7
]
,
a
d
−
b
2
=
1
a
+
b
=
3
,
b
+
d
=
7
,
(
3
−
b
)
(
7
−
b
)
−
b
2
=
1
21
−
10
b
=
1
⟶
b
=
2
,
a
=
1
,
d
=
5
A
=
[
1
2
2
5
]
,
A
−
1
=
[
5
−
2
−
2
1
]
A
−
1
=
α
A
+
β
I
[
5
−
2
−
2
1
]
=
[
α
+
β
2
α
2
α
5
α
+
β
]
α
=
−
1
,
β
=
6
⟶
α
+
β
=
5
© examsnet.com
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