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If A= \begin{bmatrix} -1 &7\\ 2& 3 \end{bmatrix}, 

Then skew symmetric part of A is?

  • Option 1)

    \begin{bmatrix} -1 &\frac{9}{2} \\ \frac{-9}{2}& 3 \end{bmatrix}

  • Option 2)

    \begin{bmatrix} -0 &\frac{-5}{2} \\ \frac{5}{2}& 0 \end{bmatrix}

  • Option 3)

    \begin{bmatrix} -1 &\frac{-9}{2} \\ \frac{9}{2}& 3 \end{bmatrix}

  • Option 4)

    \begin{bmatrix} 0 &\frac{5}{2} \\ \frac{-5}{2}& 0 \end{bmatrix}

 

Answers (1)

As learnt in concept

Skew symmetric matrix -

If A=\left [ a_{ij} \right ]  and  a_{ij}=-a_{ji}  for all i and j

- wherein

 

 Skew symmetric portion is : \left ( \frac{A-A^{T}}{2} \right )

A^{T}= \begin{bmatrix} -1 & 2\\ 7 &3 \end{bmatrix}

= \frac{1}{2}(\begin{bmatrix} -1 &7 \\ 2 &3 \end{bmatrix}- \begin{bmatrix} -1 &2 \\ 7& 3 \end{bmatrix})= \frac{1}{2}\begin{bmatrix} 0 &5 \\ -5 & 0 \end{bmatrix}

= \begin{bmatrix} 0 &\frac{5}{2} \\ \frac{-5}{2}&0 \end{bmatrix}

 


Option 1)

\begin{bmatrix} -1 &\frac{9}{2} \\ \frac{-9}{2}& 3 \end{bmatrix}

Incorrect option 

Option 2)

\begin{bmatrix} -0 &\frac{-5}{2} \\ \frac{5}{2}& 0 \end{bmatrix}

Incorrect option 

Option 3)

\begin{bmatrix} -1 &\frac{-9}{2} \\ \frac{9}{2}& 3 \end{bmatrix}

Option 4)

\begin{bmatrix} 0 &\frac{5}{2} \\ \frac{-5}{2}& 0 \end{bmatrix}

Correct option 

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Vakul

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