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UPSC NDA II 2015 Mathematics Solved Paper
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© examsnet.com
Question : 2
Total: 120
The matrix
A
=
[
1
3
2
1
x
−
1
1
2
7
x
−
3
]
will have inverse for every real number x except for
[NDA II 2015]
x
=
11
±
√
5
2
x
=
9
±
√
5
2
x
=
11
±
√
3
2
x
=
9
±
√
3
2
Validate
Solution:
A
=
[
1
3
2
1
x
−
1
1
2
7
x
−
3
]
|
A
|
=
1
[
(
x
−
1
)
(
x
−
3
)
−
7
]
−
3
[
(
x
−
3
)
−
2
]
+
2
[
7
−
2
(
x
−
1
)
]
=
x
2
−
11
x
+
29
If inverse will not exist then
|
A
|
=
0
x
2
−
11
x
+
29
=
0
x
=
11
±
√
5
2
© examsnet.com
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