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JEE Main Math Class 12 Matrices Part 2 Questions
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© examsnet.com
Question : 13
Total: 35
Let
A
be a
2
×
2
real matrix and
I
be the identity matrix of order 2 . If the roots of the equation
|
A
−
x
I
|
=
0
be -1 and 3 , then the sum of the diagonal elements of the matrix
A
2
is...............
[27-Jan-2024 Shift 2]
Your Answer:
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Solution:
👈: Video Solution
|
A
−
x
I
|
=
0
Roots are -1 and 3
Sum of roots
=
tr
(
A
)
=
2
Product of roots
=
|
A
|
=
−
3
Let
A
=
[
a
b
c
d
]
We have
a
+
d
=
2
a
d
−
b
c
=
−
3
A
2
=
[
a
b
c
d
]
×
[
a
b
c
d
]
=
[
a
2
+
b
c
a
b
+
b
d
a
c
+
c
d
b
c
+
d
2
]
We need
a
2
+
b
c
+
b
c
+
d
2
=
a
2
+
2
b
c
+
d
2
=
(
a
+
d
)
2
−
2
a
d
+
2
b
c
=
4
−
2
(
a
d
−
b
c
)
=
4
−
2
(
−
3
)
=
4
+
6
=
10
© examsnet.com
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