If A = [ 1 1 2 0] then verify that A – At is skew-symmetric
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1
Answer:
Step-by-step explanation:
A=
⎣
⎢
⎢
⎡
2
−1
0
1
0
1
1
2
3
⎦
⎥
⎥
⎤
A
T
=
⎣
⎢
⎢
⎡
2
1
1
−1
0
2
0
1
3
⎦
⎥
⎥
⎤
A−A
T
=
⎣
⎢
⎢
⎡
2
−1
0
1
0
1
1
2
3
⎦
⎥
⎥
⎤
−
⎣
⎢
⎢
⎡
2
−1
1
−1
0
2
0
1
3
⎦
⎥
⎥
⎤
=
⎣
⎢
⎢
⎡
2−2
−1−1
0−1
1−(−1)
0−0
1−2
1−0
2−1
3−3
⎦
⎥
⎥
⎤
=
⎣
⎢
⎢
⎡
0
−2
−1
2
0
−1
1
1
0
⎦
⎥
⎥
⎤
∴(A+A
T
)
T
=
⎣
⎢
⎢
⎡
0
2
1
−2
0
1
−1
−1
0
⎦
⎥
⎥
⎤
=−
⎣
⎢
⎢
⎡
0
−2
−1
2
0
−1
1
1
0
⎦
⎥
⎥
⎤
∴(A+B
T
)
T
=−(A−A
T
)
So, A−A
T
is skew symmetric matrix. Proved.
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