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  • The matrix [0 -5 8] is a A. diagonal matrix B. symmetric matrix C. skew symmetric matrix D. scalar matrix

The matrix \begin{bmatrix} 0 &-5 &8 \\5 &0 &12 \\-8 &-12 &0 \end{bmatrix} is a
A. diagonal matrix
B. symmetric matrix
C. skew symmetric matrix
D. scalar matrix

 

Answers (1)

Let A =  \begin{bmatrix} 0 &-5 &8 \\5 &0 &12 \\-8 &-12 &0 \end{bmatrix}

\mathrm{A}^{\prime}=\left[\begin{array}{ccc} 0 & -5 & 8 \\ 5 & 0 & 12 \\ -8 & -12 & 0 \end{array}\right]^{\mathrm{T}}=\left[\begin{array}{ccc} 0 & 5 & -8 \\ -5 & 0 & -12 \\ 8 & 12 & 0 \end{array}\right]=-\mathrm{A}

As A^T = -A

∴ It is skew - symmetric matrix.

Hence, we can say that,

∴ Option(C) is the correct answer.

Posted by

infoexpert22

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