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KEAM 2023 Math Solved Paper
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© examsnet.com
Question : 14
Total: 120
If
A
=
[
5
a
−
b
3
2
]
and
A
⋅
a
d
j
A
=
A
A
T
, then which of the following statements is true
5
a
−
b
=
−
5
5
a
+
b
=
10
det
(
A
)
<
0
A
is symmetric
det
(
A
)
≥
0
Validate
Solution:
A
=
[
5
a
−
b
3
2
]
A
adj
A
=
A
A
⊤
A
−
1
A
adj
A
=
A
−
1
A
A
⊤
adj
A
=
A
⊤
[
2
b
−
3
5
a
]
=
[
5
a
3
−
b
2
]
⇒
b
=
3
,
a
=
2
5
,
5
a
−
b
=
2
−
3
=
−
1
≠
−
5
5
a
+
b
=
5
≠
10
∴
A
=
[
2
−
3
3
2
]
.
A
is not symmetric
|
A
|
=
4
+
9
=
13
∴
det
(
A
)
≥
0
© examsnet.com
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