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Recent questions tagged eigenvalues
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GATE EC 2021  Question: 36
A real $2\times2$ nonsingular matrix $A$ with repeated eigenvalue is given as $A=\begin{bmatrix} x & 3.0\\ 3.0 & 4.0 \end{bmatrix}$ where $x$ is a real positive number. The value of $x$ (rounded off to one decimal place) is ________________
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Feb 20
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Linear Algebra
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Arjun
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2
GATE ECE 2019  Question: 17
The number of distinct eigenvalues of the matrix $A=\begin{bmatrix} 2&2&3&3\\0&1&1&1\\0&0&3&3\\0&0&0&2 \end{bmatrix}$ is equal to ____________.
asked
Feb 12, 2019
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Linear Algebra
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Arjun
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59
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gate2019ec
numericalanswers
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3
GATE ECE 2016 Set 2  Question: 1
The value of $x$ for which the matrix $A= \begin{bmatrix} 3& 2 &4 \\ 9& 7 & 13\\ 6&4 &9+x \end{bmatrix}$ has zero as an eigenvalue is ________
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Mar 28, 2018
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Linear Algebra
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Milicevic3306
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18
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gate2016ec2
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4
GATE ECE 2015 Set 2  Question: 2
The value of $x$ for which all the eigenvalues of the matrix given below are real is $\begin{bmatrix} 10&5+j &4 \\ x&20 &2 \\4 &2 &10 \end{bmatrix}$ $5+j$ $5j$ $15j$ $1+5j$
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Mar 28, 2018
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Linear Algebra
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11
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gate2015ec2
linearalgebra
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5
GATE ECE 2015 Set 1  Question: 5
The value of $p$ such that the vector $\begin{bmatrix} 1 \\ 2 \\ 3 \end{bmatrix}$ is an eigenvector of the matrix $\begin{bmatrix} 4 & 1 & 2 \\ p & 2 & 1 \\ 14 & 4 & 10 \end{bmatrix}$ is _________.
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Mar 28, 2018
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Linear Algebra
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Milicevic3306
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13
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gate2015ec1
numericalanswers
linearalgebra
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6
GATE ECE 2014 Set 3  Question: 27
Which one of the following statements is NOT true for a square matrix $A$? If $A$ is upper triangular, the eigenvalues of $A$ are the diagonal elements of it If $A$ is real symmetric, the eigenvalues of $A$ are always real and positive If $A$ ... $A$ are positive, all the eigenvalues of $A$ are also positive
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Mar 26, 2018
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Linear Algebra
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Milicevic3306
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17
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gate2014ec3
linearalgebra
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7
GATE ECE 2014 Set 1  Question: 4
A real $(4 \times 4)$ matrix $A$ satisfies the equation $A^{2} = I$, where $I$ is the $(4 \times 4)$ identity matrix. The positive eigen value of $A$ is ______.
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Mar 26, 2018
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Linear Algebra
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Milicevic3306
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24
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gate2014ec1
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8
GATE ECE 2013  Question: 19
The minimum eigenvalue of the following matrix is $\begin{bmatrix} 3& 5& 2\\5 &12 &7 \\2 &7 & 5\end{bmatrix}$ $0$ $1$ $2$ $3$
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Mar 26, 2018
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135
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gate2013ec
linearalgebra
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9
GATE ECE 2018  Question: 11
Let $\text{M}$ be a real $4\times 4$ matrix. Consider the following statements: $S1: M $ has $4$ linearly independent eigenvectors. $S2: M$ has $4$ distinct eigenvalues. $S3: M$ is nonsingular (invertible). Which one among the following is TRUE? $S1$ implies $S2$ $S1$ implies $S3$ $S2$ implies $S1$ $S3$ implies $S2$
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Feb 19, 2018
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Linear Algebra
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gatecse
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35
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gate2018ec
linearalgebra
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10
GATE ECE 2017 Set 1  Question: 1
Consider the 5 $\times$ 5 matrix $\begin{bmatrix} 1&2&3&4&5\\ 5&1 &2& 3 &4\\ 4&5&1&2&3\\ 3&4&5&1&2\\ 2&3&4&5&1 \end{bmatrix}$ It is given that A has only one real eigenvalue. Then the real eigenvalue of A is $2.5$ $0$ $15$ $25$
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Nov 17, 2017
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Linear Algebra
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admin
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135
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gate2017ec1
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