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AP EAPCET 25-Aug-2021 Shift 2 Paper
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© examsnet.com
Question : 9
Total: 160
Let
A
=
[
1
3
4
−
3
]
. Let
S
=
{
[
x
y
]
∈
R
2
∕
A
[
x
y
]
=
3
[
x
y
]
}
what is the cardinality of
S
?
1
Countably infinite
|
S
|
>
1
but
S
is finite
Uncountable
Validate
Solution:
👈: Video Solution
Given
A
=
[
1
3
4
−
3
]
S
=
{
[
x
y
]
∈
R
2
|
A
[
x
y
]
=
3
[
x
y
]
}
To Find
Cardinality of S
∵
A
[
x
y
]
=
3
[
x
y
]
[
1
3
4
−
3
]
[
x
y
]
=
[
3
x
3
y
1
]
⇒
[
x
+
3
y
4
x
−
3
y
]
=
[
3
x
3
y
]
⇒
x
+
3
y
=
3
x
and
4
x
−
3
y
=
3
y
⇒
2
x
=
3
y
x
=
3
y
2
∴
S
=
{
[
3
y
2
y
]
∈
R
2
|
A
[
x
y
]
=
3
[
x
y
]
}
=
{
y
[
3
2
1
]
∈
R
2
|
A
[
x
y
]
=
3
[
x
y
]
}
∵ y ∈ R
∴ |S| = R
⇒ Cardinality of S is uncountable.
© examsnet.com
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