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Question: Answered & Verified by Expert
If $A=\left[\begin{array}{ccc}\cos \theta & -\sin \theta & 0 \\ \sin \theta & \cos \theta & 0 \\ 0 & 0 & 1\end{array}\right]$, the cofactor of $a_{32}$ are
MathematicsDeterminantsJEE Main
Options:
  • A $1,-1$
  • B 0,1
  • C $-1,0$
  • D 0,0
Solution:
2061 Upvotes Verified Answer
The correct answer is: 0,0
We have,
$A=\left[\begin{array}{ccc}
\cos \theta & -\sin \theta & 0 \\
\sin \theta & \cos \theta & 0 \\
0 & 0 & 1
\end{array}\right]$
Minor of $a_{32}=\left|\begin{array}{cc}\cos \theta & 0 \\ \sin \theta & 0\end{array}\right|=0-0=0$ and cofactor of $a_{32}=-$ Minor of $a_{32}=-0=0$

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