Question

If A=[0 2x-3 x+2 0] is a skew - symmetric matrix then x is equal to:

Answer 1

$\textbf{Given:}$

$A=\left(\begin{array}{cc}0&2x-3\\x+2&0\end{array}\right)\;\text{is skew symmetric}$

$\textbf{To find:}$

$\text{The value of x}$

$\textbf{Solution:}$

$\text{We know that,}$

$\text{A square matrix A is said to be skew symmetric}$

$\text{if A=-A^T }$

$\text{Since A is skew symmetric, we have}$

$\left(\begin{array}{cc}0&2x-3\\x+2&0\end{array}\right)=-\left(\begin{array}{cc}0&2x-3\\x+2&0\end{array}\right)^T$

$\left(\begin{array}{cc}0&2x-3\\x+2&0\end{array}\right)=-\left(\begin{array}{cc}0&x+2\\2x-3&0\end{array}\right)$

$\left(\begin{array}{cc}0&2x-3\\x+2&0\end{array}\right)=\left(\begin{array}{cc}0&-x-2\\-2x+3&0\end{array}\right)$

$\text{Equating corresponding elements on bothsides, we get}$

$-2x+3=x+2$

$-2x-x=2-3$

$-3x=-1$

$3x=1$

$\implies\boxed{\bf\,x=\dfrac{1}{3}}$

$\textbf{Answer:}$

$\text{The value of x is \bf\dfrac{1}{3} }$

Find more:

If A is square matrix, then which of the following is not true ? OPTIONS --- 1) AA' is symmetric 2) A-A' is skew symmetric. 3) A square is symmetric 4) A+A' is symmetric​

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