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Byju's Answer
Standard XII
Mathematics
Adjoint of a Matrix
If A= [ 3 ...
Question
If
A
=
[
3
4
2
4
]
,
B
=
[
−
2
−
2
0
−
1
]
, then
(
A
+
B
)
−
1
=
A
is a skew-symmetric matrix
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B
A
−
1
+
B
−
1
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C
does not exist
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D
none of these
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Solution
The correct option is
D
none of these
A
=
[
3
4
2
4
]
,
B
=
[
−
2
−
2
0
−
1
]
A
+
B
=
[
1
2
2
3
]
|
A
+
B
|
=
3
−
4
=
−
1
≠
0
Hence, inverse of
(
A
+
B
)
exists.
Now,
a
d
j
(
A
+
B
)
=
C
T
=
[
3
−
2
−
2
1
]
T
⇒
a
d
j
(
A
+
B
)
=
[
3
−
2
−
2
1
]
⇒
(
A
+
B
)
−
1
=
[
−
3
2
2
−
1
]
Not a symmetric matrix.
Now, we will find
A
−
1
,
B
−
1
Here,
|
A
|
=
4
,
|
B
|
=
2
a
d
j
A
=
C
T
=
[
4
−
2
−
4
3
]
T
⇒
a
d
j
A
=
[
4
−
4
−
2
3
]
⇒
A
−
1
=
[
1
−
1
−
1
/
2
3
/
4
]
a
d
j
B
=
C
T
=
[
−
1
0
2
−
2
]
T
⇒
a
d
j
B
=
[
−
1
2
0
−
2
]
⇒
B
−
1
=
[
−
1
/
2
1
0
−
1
]
Hence,
A
−
1
+
B
−
1
=
[
1
−
1
−
1
/
2
3
/
4
]
+
[
−
1
/
2
1
0
−
1
]
=
[
1
/
2
0
−
1
/
2
−
1
/
4
]
Therefore,
(
A
+
B
)
−
1
≠
A
−
1
+
B
−
1
Hence, option 'D' is correct.
Suggest Corrections
0
Similar questions
Q.
If
A
=
3
4
2
4
,
B
=
-
2
-
2
0
-
1
,
then
A
+
B
-
1
=
(a) is a skew-symmetric matrix
(b) A
−1
+ B
−1
(c) does not exist
(d) none of these
Q.
If
A
and
B
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is
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=
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+
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, where
A
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.
Q.
If the matrix
[
2
3
5
−
1
]
=
A
+
B
, where A is symmetric and B is skew symmetric, then B = ______
Q.
If
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⎡
⎢
⎣
0
a
+
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b
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2
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