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JEE Main Math Class 12 Matrices Part 1 Questions
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© examsnet.com
Question : 29
Total: 100
Let
X
=
[
1
1
1
]
and
A
−
[
−
1
2
3
0
1
6
0
0
−
1
]
. For
k
∈
N
, if
X
′
A
k
X
−
33
, then
k
is equal to ________.
[29-Jul-2022-Shift-2]
Your Answer:
Validate
Solution:
X
=
[
1
1
1
]
;
A
=
[
−
1
2
3
0
1
6
0
0
−
1
]
X
T
A
K
X
=
33
[
1
1
1
]
[
−
1
2
3
0
1
6
0
0
−
1
]
k
[
1
1
1
]
=
33
[
1
1
1
]
[
−
1
2
3
0
1
6
0
0
−
1
]
[
1
1
1
]
=
33
As
A
2
=
[
−
1
2
3
0
1
6
0
0
−
1
]
[
−
1
2
3
0
1
6
0
0
−
1
]
=
[
1
0
6
0
1
0
0
0
1
]
A
4
=
[
1
0
6
0
1
0
0
0
1
]
[
1
0
6
0
1
0
0
0
1
]
=
[
1
0
12
0
1
0
0
0
1
]
A
8
=
[
1
0
24
0
1
0
0
0
1
]
A
10
=
[
1
0
6
0
1
0
0
0
1
]
[
1
0
24
0
1
0
0
0
1
]
=
[
1
0
30
0
1
0
0
0
1
]
for
K
→
Even
A
K
=
[
1
0
3
K
0
1
0
0
0
1
]
X
T
A
K
X
=
33
(This is not correct)
[
1
1
1
]
[
1
0
3
K
0
1
0
0
0
1
]
[
1
1
1
]
=
[
1
1
3
K
+
1
]
[
1
1
1
]
=
[
3
K
+
3
]
∴
3
K
+
3
=
33
∴
K
=
10
But it should be dropped as 33 is not matrix
If
K
is odd
X
T
A
K
X
=
33
X
T
AA
K
−
1
X
=
33
[
1
1
1
]
[
−
1
2
3
0
1
6
0
0
−
1
]
[
1
0
3
k
−
3
0
1
0
0
0
1
]
[
1
1
1
]
=
33
[
−
1
3
8
]
[
3
k
−
2
1
1
]
=
[
33
]
[
−
3
k
+
13
]
=
[
33
]
k
=
20
∕
3
(not possible)
© examsnet.com
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