GATE (TF) Textile 2012 Question Paper Solution | GATE/2012/TF/31

Question 31 (Textile Engineering & Fibre Science)

Consider the following Assertion [a] and Reason [r]
[a] M is an orthogonal matrix, but not a skew-symmetric matrix.

    \[M=\begin{bmatrix} 1 & 0 & 0\\ 0 & \cos\theta & -\sin\theta\\ 0 & \sin\theta & \cos\theta\end{bmatrix}\]


[r] Because M^{T}=M^{-1} and M^{T}\neq -M.

(A)[a] is right [r] is wrong
(B)[a] is right [r] is right
(C)[a] is wrong [r] is right
(D)[a] is wrong [r] is wrong
Answer / Solution

    \[M=\begin{bmatrix} 1 & 0 & 0\\ 0 & \cos\theta & -\sin\theta\\ 0 & \sin\theta & \cos\theta\end{bmatrix}\]


M will be orthogonal matrix when-
M \times M^T=I
T for transpose of the matrix
Here, a is right and r is wrong

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