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JEE Main Math Class 12 Matrices Part 1 Questions
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© examsnet.com
Question : 5
Total: 100
Let
α
and
β
be real numbers. Consider a
3
×
3
matrix
A
such that
A
2
=
3
A
+
α
I
. If
A
4
=
21
A
+
β
I
, then
[29-Jan-2023 Shift 1]
α
=
1
α
=
4
β
=
8
β
=
−
8
Validate
Solution:
A
2
=
3
A
+
α
I
A
3
=
3
A
2
+
α
A
A
3
=
3
(
3
A
+
α
I
)
+
α
A
A
3
=
9
A
+
α
A
+
3
α
I
A
4
=
(
9
+
α
)
A
2
+
3
α
A
=
(
9
+
α
)
(
3
A
+
α
I
)
+
3
α
A
=
A
(
27
+
6
α
)
+
α
(
9
+
α
)
⇒
27
+
6
α
=
21
⇒
α
=
−
1
⇒
β
=
α
(
9
+
α
)
=
−
8
© examsnet.com
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