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Recent questions tagged eigen-values

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GATE Chemical 2026 | Question: 13
Which one of the following is the pair of eigenvalues of the matrix $\left[\begin{array}{cc}-3 & 4 \\ 4 & 3\end{array}\right]?$$-7,7$$-5,5$$-4,3$$-3,4$
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GATE Chemical 2024 | Question: 20
Consider a matrix $\text{A}=\left[\begin{array}{cc}-5 & a \\ -2 & -2\end{array}\right]$, where $a$ is a constant. If the eigenvalues of $\text{A}$ are $-1$ and $-6$, then...
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GATE Chemical 2020 | Question: 25
Sum of the eigenvalues of the matrix $\begin{bmatrix} 2 & 4 & 6 \\ 3 & 5 & 9 \\ 12 & 1 & 7 \end{bmatrix}$ is ______ (round off to nearest integer).
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GATE Chemical 2019 | Question: 22
The product of the eigenvalues of the matrix $\begin{pmatrix} 2 &3 \\ 0& 7 \end{pmatrix}$ is ____________ (rounded off to one decimal place).
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GATE Chemical 2015 | Question: 12
For the matrix $\begin{pmatrix} 4 & 3\\ 3& 4 \end{pmatrix}$, if $\begin{pmatrix} 1\\ 1 \end{pmatrix}$ is an eigenvector, the corresponding eigenvalue is __________ .
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GATE Chemical 2013 | Question: 3
Which of the following statements are TRUE?P.The eigenvalues of a symmetric matrix are realQ.The value of the determinant of an orthogonal matrix can only be +1R.The tr...
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GATE Chemical 2012 | Question: 5
Consider the following $(2\times2)$ matrix $\left( \begin{array}{c} 4 & 0 \\ 0 & 4 \end{array} \right)$Whi...
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