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JEE Main Math Class 12 Matrices Part 2 Questions
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© examsnet.com
Question : 2
Total: 35
Let
A
be a
3
×
3
matrix of non-negative real elements such that
A
[
1
1
1
]
=
3
[
1
1
1
]
. Then the maximum value of
det
(
A
)
is _______
[4 Apr 2024 Shift 1]
Your Answer:
Validate
Solution:
👈: Video Solution
Let
A
=
[
a
1
a
2
a
3
b
1
b
2
b
3
c
1
c
2
c
3
]
A
[
1
1
1
]
=
3
[
1
1
1
]
⇒
a
1
+
a
2
+
a
3
=
3
. . . (1)
⇒
b
1
+
b
2
+
b
3
=
3
. . . (2)
⇒
c
1
+
ca
2
+
c
3
=
3
. . . (3)
Now,
|
A
|
=
(
a
1
b
2
c
3
+
a
2
b
3
c
1
+
a
3
b
1
c
2
)
−
(
a
3
b
2
c
1
+
a
2
b
1
c
3
+
a
1
b
3
c
2
)
∴
From above in formation, clearly
|
A
max
=
27
, when
a
1
=
3
,
b
2
=
3
,
c
3
=
3
© examsnet.com
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