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UPSC NDA I 2015 Mathematics Solved Paper
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© examsnet.com
Question : 23
Total: 120
Let
A
=
[
x
+
y
y
2
x
x
−
y
]
,
B
=
[
2
−
1
]
and
C
=
[
3
2
]
If AB = C, then what is
A
2
equal to?
[NDA I 2015]
[
6
−
10
4
26
]
[
−
10
5
4
24
]
[
−
5
−
6
−
4
−
20
]
[
−
5
−
7
−
5
20
]
Validate
Solution:
Consider the following matrices
A
=
(
x
+
y
y
2
x
x
−
y
)
B
=
(
2
−
1
)
A
B
=
(
x
+
y
y
2
x
x
−
y
)
(
2
−
1
)
=
(
2
x
+
2
y
−
y
4
x
−
x
+
y
)
=
(
2
x
+
y
3
x
+
y
)
=
C
=
(
3
2
)
Therefore, by comparing the elements of the matrices, we get
2
x
+
y
=
3
;
3
x
+
y
=
2
Hence Solving for x and yields
x
=
−
1
,
y
=
5
Therefore matrix A will be equal to
A
=
(
x
+
y
y
2
x
x
−
y
)
=
(
4
5
−
2
−
6
)
Hence,the required answer is
A
2
=
(
4
5
−
2
−
6
)
(
4
5
−
2
−
6
)
=
(
6
−
10
4
26
)
© examsnet.com
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