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Byju's Answer
Standard XII
Mathematics
Addition and Subtraction of a Matrix
Let A+B =I,...
Question
Let
A
+
B
=
I
, where A=
⎡
⎢
⎣
0
1
−
1
4
−
3
4
3
−
3
4
⎤
⎥
⎦
Find
B
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Solution
A
+
B
=
I
⎡
⎢
⎣
0
1
−
1
4
−
3
4
3
−
3
4
⎤
⎥
⎦
+
B
=
⎡
⎢
⎣
1
0
0
0
1
0
0
0
1
⎤
⎥
⎦
B
=
⎡
⎢
⎣
1
0
0
0
1
0
0
0
1
⎤
⎥
⎦
−
⎡
⎢
⎣
0
1
−
1
4
−
1
4
3
−
3
4
⎤
⎥
⎦
=
⎡
⎢
⎣
1
−
1
1
−
4
2
−
4
−
3
3
−
3
⎤
⎥
⎦
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Similar questions
Q.
If matrix
A
=
⎡
⎢
⎣
0
1
−
1
4
−
3
4
3
−
3
4
⎤
⎥
⎦
=
B
+
C
, where
B
is symmetric matrix and
C
is skew-symmetric matrix.
Then the matrices
B
and
C
are:
Q.
If matrix
A
=
⎡
⎢
⎣
0
1
−
1
4
−
3
4
3
−
3
4
⎤
⎥
⎦
, can be written as
B
+
C
where B is symmetric matrix and C is skew-symmetric matrix, then
B
−
C
is equal to
Q.
Let
X
be the solution set of the equation
A
x
=
I
, where
A
=
⎡
⎢
⎣
0
1
−
1
4
−
3
4
3
−
3
4
⎤
⎥
⎦
and
I
is the corresponding unit matrix and
x
∈
N
then find the minimum value of
∑
(
cos
x
θ
+
sin
x
θ
)
,
θ
∈
R
.
Q.
Let
X
be the solution set of the equation
A
x
=
I
,
where
A
=
⎡
⎢
⎣
0
1
−
1
4
−
3
4
3
−
3
4
⎤
⎥
⎦
and
I
is the corresponding unit matrix and
x
∈
N
,
then the minimum value of
∑
(
cos
x
θ
+
sin
x
θ
)
,
θ
∈
R
is
Q.
For the matrix
A
=
⎡
⎢
⎣
0
1
−
1
4
−
3
4
3
−
3
4
⎤
⎥
⎦
, the inverse of
A
2
will be
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