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JEE Main Math Class 12 Matrices Part 2 Questions
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© examsnet.com
Question : 11
Total: 35
Let
B
=
[
1
3
1
5
]
and
A
be a
2
×
2
matrix such that
AB
−
1
=
A
−
1
. If
BCB
−
1
=
A
and
C
4
+
α
C
2
+
β
I
=
O
, then
2
β
−
α
is equal to :
[9 Apr 2024 Shift 2]
16
2
8
10
Validate
Solution:
👈: Video Solution
BCB
−
1
=
A
⇒
(
BCB
−
1
)
(
BCB
−
1
)
=
A
⋅
A
⇒
BCI
CB
−
1
=
A
2
⇒
BC
2
B
−
1
=
A
2
⇒
B
−
1
(
BC
2
B
−
1
)
B
=
B
−
1
(
A
⋅
A
)
B
From equation (1)
C
2
=
A
−
1
⋅
A
⋅
B
C
2
=
B
Also
AB
−
1
=
A
−
1
⇒
AB
−
1
⋅
A
=
A
−
1
A
=
I
⇒
A
−
1
(
AB
−
1
A
)
=
A
−
1
I
B
−
1
A
=
A
−
1
Now characteristics equation of
C
2
is
|
C
2
−
λ
I
|
=
0
|
B
−
λ
I
|
=
0
⇒
|
1
−
λ
3
1
5
−
λ
|
=
0
⇒
(
1
−
λ
)
(
5
−
1
)
−
3
=
0
⇒
(
λ
2
−
6
λ
+
5
)
−
3
=
0
⇒
λ
2
−
6
λ
+
2
=
0
⇒
β
2
−
6
B
+
2
I
=
0
⇒
C
4
−
6
C
2
+
2
I
=
0
α
=
−
6
β
=
2
∴
2
β
−
α
=
4
+
6
=
10
© examsnet.com
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