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  • Given a skew-symmetric matrix <img alt="A = \begin{bmatrix} 0 &a &1 \\ -1 &b &1 \\ -1& c &0 \end{bmatrix}" src="https://learn.careers360.com/latex-image/?A%20%3D%20%5Cbegin%7Bbmatrix%7D%200%20%26a%20%261%20%5C%5C%20-1%20%26b%20%

Given a skew-symmetric matrix A = \begin{bmatrix} 0 &a &1 \\ -1 &b &1 \\ -1& c &0 \end{bmatrix} , the value of(a + b + c)^{2} is __________ .

 

 

Answers (1)

Given:

A = \begin{bmatrix} 0 &a &1 \\ -1 &b &1 \\ -1& c &0 \end{bmatrix}

A is a skew-symmetric matrix.

 A^T=-A

\begin{bmatrix} 0 &-1 &-1 \\ a &b &c \\ 1& 1 &0 \end{bmatrix}= \begin{bmatrix} 0 &-a &-1 \\ 1 &-b &-1 \\ 1& -c &0 \end{bmatrix}

-a = -1  => a = 1

b = -b =>  b=0

c = -1

(a + b + c)^{2} = (1+0-1)^2=0

Posted by

Safeer PP

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