If A is a skew-symmetric matrix of order n,an | vedclass

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(C) Let $X = C^T AC$. Since $X$ is a $1 	imes n$ matrix multiplied by an $n 	imes n$ matrix and then by an $n 	imes 1$ matrix,the resulting matrix

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$A$ zero matrix of order $1$

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(C) Let $X = C^T AC$. Since $X$ is a $1 	imes n$ matrix multiplied by an $n 	imes n$ matrix and then by an $n 	imes 1$ matrix,the resulting matrix $X$ is of order $1 	imes 1$. Taking the transpose of $X$,we get $X^T = (C^T AC)^T = C^T A^T (C^T)^T = C^T A^T C$. Since $A$ is a skew-symmetric matrix,$A^T = -A$. Therefore,$X^T = C^T (-A) C = -(C^T AC) = -X$. Since $X$ is a $1 	imes 1$ matrix,let $X = [k]$. Then $X^T = [k]$. The condition $X^T = -X$ implies $[k] = -[k]$,which means $k = -k$,so $2k = 0$,hence $k = 0$. Thus,$C^T AC$ is a zero matrix of order $1 	imes 1$.

If $A$ is a skew-symmetric matrix of order $n$,and $C$ is a column matrix of order $n \times 1$,then $C^T AC$ is

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