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Question: The matrix \(\begin{bmatrix} 0 & 5 & - 7 \\ - 5 & 0 & 11 \\ 7 & - 11 & 0 \end{bmatrix}\)is known as...

The matrix $\begin{bmatrix} 0 & 5 & - 7 \

  • 5 & 0 & 11 \ 7 & - 11 & 0 \end{bmatrix}$is known as
A

Upper triangular matrix

B

Skew-symmetric matrix

C

Symmetric matrix

D

Diagonal matrix

Answer

Skew-symmetric matrix

Explanation

Solution

In a skew-symmetric matrix, aij=−aji∀i,j=1,2,3a_{ij} = - a_{ji}\forall i,j = 1,2,3and j=ij = i, aii=−aiia_{ii} = - a_{ii} ⇒ each aii =0

Hence the given matrix is skew-symmetric matrix

[∵AT=−A]\lbrack\because A^{T} = - A\rbrack.