Out of the following which is a skew- symmetric matrix Options: A . &nbsp⎡⎢⎣045−40−6−560⎤⎥⎦ B . &nbsp⎡⎢⎣145−41−6−561⎤⎥⎦ C . &nbsp⎡⎢⎣145−42−6−563⎤⎥⎦ D . &nbsp⎡⎢⎣i+145−4i−6−56i⎤⎥⎦

Answer: Option A : A In a skew-symmetrix matrix a i j = − a j i ∀ i , j = 1 , 2 , 3 f o r j = i , a i i = − a j i ⇒ each a i i = 0 . Hence the matrix ⎡ ⎢ ⎣ 0 4 5 − 4 0 − 6 − 5 6 0 ⎤ ⎥ ⎦ is skew-symmetric.

Out of the following which is a skew- symmetric matrix

Question

Out of the following which is a skew- symmetric matrix

Options:

A . ⎡⎢⎣045−40−6−560⎤⎥⎦

B . ⎡⎢⎣145−41−6−561⎤⎥⎦

C . ⎡⎢⎣145−42−6−563⎤⎥⎦

D . ⎡⎢⎣i+145−4i−6−56i⎤⎥⎦

Answer: Option A
:
A
In a skew-symmetrix matrix

a_{i j} = - a_{j i} \forall i, j = 1, 2, 3 f o r j = i, a_{i i} = - a_{j i} \Rightarrow

each

a_{i i} = 0

.
Hence the matrix

⎡ ⎢ ⎣ \begin{matrix} 0 & 4 & 5 - 4 & 0 & - 6 - 5 & 6 & 0 \end{matrix} ⎤ ⎥ ⎦

is skew-symmetric.

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