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Question
Mathematics
If A = [6&8&5 4&2&3 9&7&1] is the sum of a symmetric matrix B and skew-symmetric matrix C, then B is
Q. If
A
=
⎣
⎡
6
4
9
8
2
7
5
3
1
⎦
⎤
is the sum of a symmetric matrix B and skew-symmetric matrix C, then B is
3747
194
Matrices
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A
⎣
⎡
6
6
7
6
2
5
7
5
1
⎦
⎤
35%
B
⎣
⎡
0
−
2
2
2
5
2
−
2
−
2
0
⎦
⎤
24%
C
⎣
⎡
6
−
6
−
7
6
2
5
7
−
5
1
⎦
⎤
31%
D
⎣
⎡
0
2
−
2
6
0
−
2
−
2
−
2
0
⎦
⎤
10%
Solution:
If
A
=
⎣
⎡
6
4
9
8
2
7
5
3
1
⎦
⎤
is the sum of a symmetric matrix B and skew symmetric matrix C,
Transpose of
A
=
⎣
⎡
6
8
5
4
2
3
9
7
1
⎦
⎤
So that
B
=
2
1
⎣
⎡
⎣
⎡
6
4
9
8
2
7
5
3
1
⎦
⎤
+
⎣
⎡
6
8
5
4
2
3
9
7
1
⎦
⎤
⎦
⎤
B
=
2
1
⎣
⎡
12
12
14
12
4
10
14
10
2
⎦
⎤
=
⎣
⎡
6
6
7
6
2
5
7
5
1
⎦
⎤