Mathematics:Teaching, Learning and Exploring.
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Q.(NET Dec 2014)
The Determinant of \(n \times n \) permutation matrix is
\[ \begin{pmatrix} 0 & 0 & \cdots & 1 \\ 0 & 0 & 1 & 0 \\ \vdots & \vdots & \ddots & \vdots \\ 1 & 0 & \cdots & 0\end{pmatrix} \]
A) \( (-1)^n \)
B) \( (-1)^{\frac{n}{2}} \)
C) \( -1 \)
D) \( 1 \)
Ans .
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Q.(NET Dec 2014)
Which of the following matrices have Jordan canonical form equal to \[ \begin{pmatrix} 0 & 1 & 0 \\ 0 & 0 & 0 \\ 0 & 0 & 0 \end{pmatrix} \]
A) \[ \begin{pmatrix} 0 & 0 & 1 \\ 0 & 0 & 0 \\ 0 & 0 & 0 \end{pmatrix} \]
B) \[ \begin{pmatrix} 0 & 0 & 1 \\ 0 & 0 & 1 \\ 0 & 0 & 0 \end{pmatrix} \]
C) \[ \begin{pmatrix} 0 & 1 & 1 \\ 0 & 0 & 0 \\ 0 & 0 & 0 \end{pmatrix} \]
D) \[ \begin{pmatrix} 0 & 1 & 1 \\ 0 & 0 & 1 \\ 0 & 0 & 0 \end{pmatrix} \]
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Q(NET DEC 2014)
Which of the following are eigenvalues of the matrix
\[ \begin{pmatrix} 0 & 0 & 0 & 1 & 0 & 0 \\
0 & 0 & 0& 0 & 1 & 0 \\
0& 0 & 0 & 0 & 0 & 0 \\
1& 0 & 0 & 0 & 0 & 0 \\
0& 0 & 0 & 0 & 0 & 0 \\
0& 0 & 1 & 0 & 0 & 0 \end{pmatrix} \]
A) 1
B)\(-1\)
C) i
D)\(-i\)
Ans
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Q.(NET Dec 2014)
The Determinant of \(n \times n \) permutation matrix is
\[ \begin{pmatrix} 0 & 0 & \cdots & 1 \\ 0 & 0 & 1 & 0 \\ \vdots & \vdots & \ddots & \vdots \\ 1 & 0 & \cdots & 0\end{pmatrix} \]
A) \( (-1)^n \)
B) \( (-1)^{\frac{n}{2}} \)
C) \( -1 \)
D) \( 1 \)Ans . \(\textbf{Option C}\)
Option C: The determinant of backward identity matrix is \( -1 \).
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