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JEE Main Math Class 12 Matrices Part 1 Questions
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© examsnet.com
Question : 34
Total: 100
Let
A
=
(
2
−
2
1
−
1
)
and
B
=
(
−
1
2
−
1
2
)
. Then the number of elements in the set
{
(
n
,
m
)
:
n
,
m
∈
{
1
,
2
,
.
.
.
.
.
.
.
.
.
,
10
}
.
and
.
n
A
n
+
m
B
m
=
1
}
is___
[25-Jun-2022-Shift-2]
Your Answer:
Validate
Solution:
A
2
=
[
2
−
2
1
−
1
]
[
2
−
2
1
−
1
]
=
[
2
−
2
1
−
1
]
=
A
⇒
A
K
=
A
,
K
∈
I
B
2
=
[
−
1
2
−
1
2
]
[
−
1
2
−
1
2
]
=
[
−
1
2
−
1
2
]
=
B
So,
B
K
=
B
,
K
∈
I
n
A
n
+
m
B
m
=
n
A
+
m
B
=
[
2
n
−
2
n
n
−
n
]
+
[
−
m
2
m
−
m
2
m
]
=
[
1
0
0
1
]
So,
2
n
−
m
=
1
,
−
n
+
m
=
0
,
2
m
−
n
=
1
So,
(
m
,
n
)
=
(
1
,
1
)
© examsnet.com
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