If the matrix A= \begin{bmatrix} 0 & a &-3 \\ 2 & 0 & -1\\ b & 1 & 0 \end{bmatrix} skew symmetric, find the values of ‘a’
and ‘b’.

 

 

 

 
 
 
 
 

Answers (1)

given A= \begin{bmatrix} 0 &a &-3 \\ 2 & 0& -1\\ b & 1 & 0 \end{bmatrix}
A is given to be skew symmetric matrix
 \therefore A^{T}= -A
\begin{bmatrix} 0 &2 &b\\ a & 0& 1\\ -3 & -1 & 0 \end{bmatrix}= - \begin{bmatrix} 0 &a &-3 \\ 2 & 0& -1\\ b & 1 & 0 \end{bmatrix}
\begin{bmatrix} 0 &2 &b\\ a & 0& 1\\ -3 & -1 & 0 \end{bmatrix}= \begin{bmatrix} 0 &-a &-3 \\ -2 & 0& 1\\ -b & -1 & 0 \end{bmatrix}
Comparing both sides we get
-a= 2 \; \S \: b= 3
   a= -2 \; \S \: b= 3
 

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