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NDA Math Determinants
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© examsnet.com
Question : 22
Total: 68
Let
A
=
[
x
+
y
y
2
x
x
−
y
]
,
B
=
[
2
−
1
]
and
C
=
[
3
2
]
. If
A
B
=
C
,
then what is the value of the determinant of the matrix
A
?
[NDA-I 2020]
-10
-14
-24
-34
Validate
Solution:
👈: Video Solution
A
B
=
[
x
+
y
y
2
x
x
−
y
]
[
2
−
1
]
=
[
2
(
x
+
y
)
−
y
4
x
−
x
+
y
]
=
[
2
x
+
y
3
x
+
y
]
As
A
B
=
C
∴
[
2
x
+
y
3
x
+
y
]
=
[
3
2
]
2
x
+
y
=
3
....(i)
and
3
x
+
y
=
2
....(ii)
From equation (i) and (ii), we get
x
=
−
1
,
y
=
5
∴
A
=
[
−
1
+
5
5
−
2
−
1
−
5
]
=
[
4
5
−
2
−
6
]
=
4
(
−
6
)
−
5
(
−
2
)
=
−
14
© examsnet.com
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