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Recent questions tagged eigen-values

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GATE Civil 2024 Set 1 | Question: 26
​​​​​What are the eigenvalues of the matrix $\left[\begin{array}{lll}2 & 1 & 1 \\ 1 & 4 & 1 \\ 1 & 1 & 2\end{array}\right]$ ?$1,2,5$1,3,4$-5,1,2$-5,-1,2$
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GATE Civil 2021 Set 2 | Question: 27
The smallest eigenvalue and the corresponding eigenvector of the matrix $\begin{bmatrix} 2 & -2 \\ -1 & 6 \end{bmatrix}$, respectively, are$1.55$ ... end{Bmatrix}$1.55$ and $\begin{Bmatrix} 2.00\\ -0.45 \end{Bmatrix}$
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GATE2020 CE-2-27
A $4 \times 4$ matrix $[P]$ is given below$[P] = \begin{bmatrix}0 &1 &3 &0 \\-2 &3 &0 &4 \\0 &0 &6 &1 \\0 &0 &1 &6 \end{bmatrix}$The eigen values of $[P]$ are $0, 3, 6, 6$1, 2, 3, 4$3, 4, 5, 7$1, 2, 5, 7$
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GATE2016-1-3
If the entries in each column of a square matrix $M$ add up to $1$, then an eigenvalue of $M$ is$4$3$2$1$
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GATE2017 CE-1: 28
Consider the matrix $\begin{bmatrix} 5 & -1 \\ 4 & 1 \end{bmatrix}$. Which one of the following statements is TRUE for the eigenvalues and ... eigenvector exists.Eigenvalues are $3$ and $-3$, and two independent eigenvectors exist.
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GATE2015-2-28
The two Eigen values of the matrix $\begin{bmatrix} 2 & 1 \\ 1 & p \end{bmatrix}$ have a ratio of $3:1$ for $p=2$. What is another value of $p$ for which the Eigen values have the same ratio of $3:1$?$-2$1$7/3$14/3$
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GATE2015-1-26
The smallest and largest Eigen values of the following matrix are:$\begin{bmatrix} 3 & -2 & 2 \\ 4 & -4 & 6 \\ 2 & -3 & 5 \end{bmatrix}$1.5$ and $2.5$0.5$ and $2.5$1.0$ and $3.0$1.0$ and $2.0$
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GATE2014-1-4
The sum of Eigen values of the matrix, $[M]$ iswhere $[M] = \begin{bmatrix} 215 & 650 & 795 \\ 655 & 150 & 835 \\ 485 & 355 & 550 \end{bmatrix}$915$1355$1640$2180$
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GATE Civil 2012 | Question: 28
The eigenvalues of matrix $\begin{bmatrix} 9 & 5 \\ 5 & 8 \end{bmatrix}$ are$-2.42$ and $6.86$3.48$ and $13.53$4.70$ and $6.86$6.86$ and $9.50$
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GATE2018 CE-2: 26
The matrix $\begin{pmatrix} 2 & -4 \\ 4 & -2 \end{pmatrix}$ hasreal eigenvalues and eigenvectorsreal eigenvalues but complex eigenvectorscomplex eigenvalues but real eigenvectorscomplex eigenvalues and eigenvectors
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