The matrix is a

Engineering

Mathematics

Special Type of Square Matrices

Symmetric and Skew Symmetric Matrices

Question

The matrix $[\begin{array}{ccc} 0 & 5 & 8 \\ - 5 & 0 & 12 \\ - 8 & - 12 & 0 \end{array}]$ is a

diagonal matrix

symmetric matrix

skew symmetric matrix

scalar matrix

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We know, that in a square matrix, if b_ij = 0, when i ≠ j, then it is said to be a diagonal matrix. Here, b₁₂, b₁₃ ...... ≠ 0 so, the given matrix is not a diagonal matrix.

Now

B = [\begin{array}{ccc} 0 & 5 & 8 \\ - 5 & 0 & 12 \\ - 8 & - 12 & 0 \end{array}]

∴ B^{T} = B^{'} = [\begin{array}{ccc} 0 & - 5 & - 8 \\ 5 & 0 & - 12 \\ 8 & 12 & 0 \end{array}] = - [\begin{array}{ccc} 0 & 5 & 8 \\ 5 & 0 & 12 \\ - 8 & - 12 & 0 \end{array}] = - B

So, the given matrix is a skew symmetric matrix, since we know that in a square matrix B, if B' = – B, then it is called skew symmetric matrix.