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Search results for eigen-value
88
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6
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1
GATE CSE 2017 Set 1 | Question: 31
Let $A$ be $n\times n$ real valued square symmetric matrix of rank $2$ with $\sum_{i=1}^{n}\sum_{j=1}^{n}A^{2}_{ij} = 50.$ Consider the following statements. One eigenvalue must be in $\left [ -5,5 \right ]$ The eigenvalue ... than $5$ Which of the above statements about eigenvalues of $A$ is/are necessarily CORRECT? Both I and II I only II only Neither I nor II
Let $A$ be $n\times n$ real valued square symmetric matrix of rank $2$ with $\sum_{i=1}^{n}\sum_{j=1}^{n}A^{2}_{ij} = 50.$ Consider the following statements.One eigenvalu...
Arjun
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Arjun
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Feb 14, 2017
Linear Algebra
gatecse-2017-set1
linear-algebra
eigen-value
normal
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–
99
votes
8
answers
2
GATE CSE 2014 Set 2 | Question: 47
The product of the non-zero eigenvalues of the matrix is ____ $\begin{pmatrix} 1 & 0 & 0 & 0 & 1 \\ 0 & 1 & 1 & 1 & 0 \\ 0 & 1 & 1 & 1 & 0 \\ 0 & 1 & 1 & 1 & 0 \\ 1 & 0 & 0 & 0 & 1 \end{pmatrix}$
The product of the non-zero eigenvalues of the matrix is ____$\begin{pmatrix} 1 & 0 & 0 & 0 & 1 \\ 0 & 1 & 1 & 1 & 0 \\ 0 & 1 & 1 & 1 & 0 \\ 0 & 1 & 1 & 1 & 0 \\ 1 & 0 & ...
go_editor
37.4k
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go_editor
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Sep 28, 2014
Linear Algebra
gatecse-2014-set2
linear-algebra
eigen-value
normal
numerical-answers
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79
votes
7
answers
3
GATE CSE 2018 | Question: 26
Consider a matrix P whose only eigenvectors are the multiples of $\begin{bmatrix} 1 \\ 4 \end{bmatrix}$. Consider the following statements. P does not have an inverse P has a repeated eigenvalue P cannot be diagonalized Which one of the ... III are necessarily true Only II is necessarily true Only I and II are necessarily true Only II and III are necessarily true
Consider a matrix P whose only eigenvectors are the multiples of $\begin{bmatrix} 1 \\ 4 \end{bmatrix}$.Consider the following statements.P does not have an inverseP has ...
gatecse
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gatecse
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Feb 14, 2018
Linear Algebra
gatecse-2018
linear-algebra
matrix
eigen-value
normal
2-marks
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–
18
votes
5
answers
4
GATE CSE 2021 Set 1 | Question: 52
Consider the following matrix.$\begin{pmatrix} 0 & 1 & 1 & 1\\ 1& 0& 1 & 1\\ 1& 1 & 0 & 1 \\1 & 1 & 1 & 0 \end{pmatrix}$The largest eigenvalue of the above matrix is __________.
Consider the following matrix.$$\begin{pmatrix} 0 & 1 & 1 & 1\\ 1& 0& 1 & 1\\ 1& 1 & 0 & 1 \\1 & 1 & 1 & 0 \end{pmatrix}$$The largest eigenvalue of the above matrix is __...
Arjun
15.6k
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Arjun
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Feb 18, 2021
Linear Algebra
gatecse-2021-set1
linear-algebra
matrix
eigen-value
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2-marks
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9
votes
4
answers
5
GATE CSE 2023 | Question: 20
Let $A$ be the adjacency matrix of the graph with vertices $\{1,2,3,4,5\}.$ Let $\lambda_{1}, \lambda_{2}, \lambda_{3}, \lambda_{4}$, and $\lambda_{5}$ be the five eigenvalues of $A$. Note that these eigenvalues need not be distinct. The value of $\lambda_{1}+\lambda_{2}+\lambda_{3}+\lambda_{4}+\lambda_{5}=$____________
Let $A$ be the adjacency matrix of the graph with vertices $\{1,2,3,4,5\}.$Let $\lambda_{1}, \lambda_{2}, \lambda_{3}, \lambda_{4}$, and $\lambda_{5}$ be the five eigenva...
admin
13.1k
views
admin
asked
Feb 15, 2023
Linear Algebra
gatecse-2023
linear-algebra
eigen-value
numerical-answers
1-mark
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47
votes
8
answers
6
GATE CSE 2017 Set 2 | Question: 52
If the characteristic polynomial of a $3 \times 3$ matrix $M$ over $\mathbb{R}$ (the set of real numbers) is $\lambda^3 – 4 \lambda^2 + a \lambda +30, \quad a \in \mathbb{R}$, and one eigenvalue of $M$ is $2,$ then the largest among the absolute values of the eigenvalues of $M$ is _______
If the characteristic polynomial of a $3 \times 3$ matrix $M$ over $\mathbb{R}$ (the set of real numbers) is $\lambda^3 – 4 \lambda^2 + a \lambda +30, \quad a \in \ma...
Madhav
15.6k
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Madhav
asked
Feb 14, 2017
Linear Algebra
gatecse-2017-set2
engineering-mathematics
linear-algebra
numerical-answers
eigen-value
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81
votes
5
answers
7
GATE CSE 2007 | Question: 25
Let A be a $4 \times 4$ matrix with eigen values -5,-2,1,4. Which of the following is an eigen value of the matrix$\begin{bmatrix} A & I \\ I & A \end{bmatrix}$, where $I$ is the $4 \times 4$ identity matrix? $-5$ $-7$ $2$ $1$
Let A be a $4 \times 4$ matrix with eigen values -5,-2,1,4. Which of the following is an eigen value of the matrix$\begin{bmatrix} A & I \\ I & A \end{bmatrix}$, where $...
priya
16.8k
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priya
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Sep 2, 2014
Linear Algebra
gatecse-2007
eigen-value
linear-algebra
difficult
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49
votes
10
answers
8
GATE CSE 2016 Set 1 | Question: 05
Two eigenvalues of a $3 \times 3$ real matrix $P$ are $(2+\sqrt {-1})$ and $3$. The determinant of $P$ is _______
Two eigenvalues of a $3 \times 3$ real matrix $P$ are $(2+\sqrt {-1})$ and $3$. The determinant of $P$ is _______
Sandeep Singh
14.7k
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Sandeep Singh
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Feb 12, 2016
Linear Algebra
gatecse-2016-set1
linear-algebra
eigen-value
numerical-answers
normal
+
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61
votes
8
answers
9
GATE IT 2007 | Question: 2
Let $A$ be the matrix $\begin{bmatrix}3 &1 \\ 1&2\end{bmatrix}$. What is the maximum value of $x^TAx$ where the maximum is taken over all $x$ that are the unit eigenvectors of $A?$ $5$ $\frac{(5 + √5)}{2}$ $3$ $\frac{(5 - √5)}{2}$
Let $A$ be the matrix $\begin{bmatrix}3 &1 \\ 1&2\end{bmatrix}$. What is the maximum value of $x^TAx$ where the maximum is taken over all $x$ that are the unit eigenvect...
Ishrat Jahan
16.3k
views
Ishrat Jahan
asked
Oct 29, 2014
Linear Algebra
gateit-2007
linear-algebra
eigen-value
normal
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–
31
votes
9
answers
10
GATE CSE 2015 Set 3 | Question: 15
In the given matrix $\begin{bmatrix} 1 & -1 & 2 \\ 0 & 1 & 0 \\ 1 & 2 & 1 \end{bmatrix}$ , one of the eigenvalues is $1.$ The eigenvectors corresponding to the eigenvalue $1$ ... $\left\{a\left(- \sqrt{2},0,1\right) \mid a \neq 0, a \in \mathbb{R}\right\}$
In the given matrix $\begin{bmatrix} 1 & -1 & 2 \\ 0 & 1 & 0 \\ 1 & 2 & 1 \end{bmatrix}$ , one of the eigenvalues is $1.$ The eigenvectors corresponding to the eigenvalue...
go_editor
17.7k
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go_editor
asked
Feb 14, 2015
Linear Algebra
gatecse-2015-set3
linear-algebra
eigen-value
normal
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24
votes
6
answers
11
GATE CSE 2018 | Question: 17
Consider a matrix $A= uv^T$ where $u=\begin{pmatrix}1 \\ 2 \end{pmatrix} , v = \begin{pmatrix}1 \\1 \end{pmatrix}$. Note that $v^T$ denotes the transpose of $v$. The largest eigenvalue of $A$ is ____
Consider a matrix $A= uv^T$ where $u=\begin{pmatrix}1 \\ 2 \end{pmatrix} , v = \begin{pmatrix}1 \\1 \end{pmatrix}$. Note that $v^T$ denotes the transpose of $v$. The larg...
gatecse
10.3k
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gatecse
asked
Feb 14, 2018
Linear Algebra
gatecse-2018
linear-algebra
eigen-value
normal
numerical-answers
1-mark
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49
votes
7
answers
12
GATE CSE 1993 | Question: 01.1
The eigen vector $(s)$ of the matrix $\begin{bmatrix} 0 &0 &\alpha\\ 0 &0 &0\\ 0 &0 &0 \end{bmatrix},\alpha \neq 0$ is (are) $(0,0,\alpha)$ $(\alpha,0,0)$ $(0,0,1)$ $(0,\alpha,0)$
The eigen vector $(s)$ of the matrix $$\begin{bmatrix} 0 &0 &\alpha\\ 0 &0 &0\\ 0 &0 &0 \end{bmatrix},\alpha \neq 0$$ is (are)$(0,0,\alpha)$$(\alpha,0,0)$$(0,0,1)$$(0,\al...
Kathleen
11.6k
views
Kathleen
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Sep 13, 2014
Linear Algebra
gate1993
eigen-value
linear-algebra
easy
multiple-selects
+
–
26
votes
1
answer
13
GATE CSE 2022 | Question: 43
Which of the following is/are the eigenvector(s) for the matrix given below? $\begin{pmatrix} - 9 & - 6 & - 2 & - 4 \\ - 8 & - 6 & - 3 & - 1 \\ 20 & 15 & 8 & 5 \\ 32 & 21 & 7 & 12 \end{pmatrix}$ ... $\begin{pmatrix} - 1 \\ 0 \\ 2 \\ 2 \end{pmatrix}$ $\begin{pmatrix} 0 \\ 1 \\ - 3 \\ 0 \end{pmatrix}$
Which of the following is/are the eigenvector(s) for the matrix given below?$$\begin{pmatrix} – 9 & – 6 & – 2 & – 4 \\ – 8 & – 6 & – 3 & – ...
Arjun
10.4k
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Arjun
asked
Feb 15, 2022
Linear Algebra
gatecse-2022
linear-algebra
eigen-value
multiple-selects
2-marks
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–
26
votes
4
answers
14
GATE CSE 2019 | Question: 44
Consider the following matrix: $R = \begin{bmatrix} 1 & 2 & 4 & 8 \\ 1 & 3 & 9 & 27 \\ 1 & 4 & 16 & 64 \\ 1 & 5 & 25 & 125 \end{bmatrix}$ The absolute value of the product of Eigen values of $R$ is _______
Consider the following matrix:$R = \begin{bmatrix} 1 & 2 & 4 & 8 \\ 1 & 3 & 9 & 27 \\ 1 & 4 & 16 & 64 \\ 1 & 5 & 25 & 125 \end{bmatrix}$The absolute value of the product ...
Arjun
19.6k
views
Arjun
asked
Feb 7, 2019
Linear Algebra
gatecse-2019
numerical-answers
engineering-mathematics
linear-algebra
eigen-value
2-marks
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27
votes
3
answers
15
GO Classes CS/DA 2025 | Weekly Quiz 4 | Linear Algebra | Question: 14
Mark all the INCORRECT statements Let $A$ be the matrix of a rotation by angle $30$ degree. That is, for any vector $x,$ the angle between $x$ and $A x$ is always $30$ degree. Then $A$ ... $\lambda=1,2,3$, then $A$ is singular. If $A$ is a symmetric matrix, then all its eigenvectors are orthogonal.
Mark all the INCORRECT statementsLet $A$ be the matrix of a rotation by angle $30$ degree. That is, for any vector $x,$ the angle between $x$ and $A x$ is always $30$ deg...
GO Classes
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views
GO Classes
asked
Mar 29, 2023
Linear Algebra
goclasses2025_csda_wq4
goclasses
linear-algebra
eigen-value
multiple-selects
1-mark
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4
votes
1
answer
16
GO Classes Test Series 2024 | Mock GATE | Test 11 | Question: 30
Let $A$ be a matrix defined as $A=u v^T$, where $u$ and $v$ are column vectors of dimension $3 \times 1$. The resulting matrix $A$ will be of dimension $3 \times 3$. What are the maximum number of nonzero eigenvalues possible for the matrix $A?$
Let $A$ be a matrix defined as $A=u v^T$, where $u$ and $v$ are column vectors of dimension $3 \times 1$. The resulting matrix $A$ will be of dimension $3 \times 3$. What...
GO Classes
774
views
GO Classes
asked
Jan 13
Linear Algebra
goclasses2024-mockgate-11
goclasses
numerical-answers
linear-algebra
eigen-value
1-mark
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7
votes
3
answers
17
GO Classes CS/DA 2025 | Weekly Quiz 5 | Linear Algebra | Question: 2
Let $M$ be a $2 \times 2$ matrix with the property that the sum of each of the rows and also the sum of each of the columns is the same constant $c$. Which (if any) any of the vectors must be an eigenvector of $M$ ... $W = \left[\begin{array}{l}1 \\ 1 \\ \end{array}\right]$ $U$ $V$ $W$ None of the above
Let $M$ be a $2 \times 2$ matrix with the property that the sum of each of the rowsand also the sum of each of the columns is the same constant $c$. Which (if any) any of...
GO Classes
106
views
GO Classes
asked
Apr 3
Linear Algebra
goclasses2025_csda_wq5
goclasses
linear-algebra
matrix
eigen-value
easy
1-mark
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3
votes
2
answers
18
GO Classes CS/DA 2025 | Weekly Quiz 5 | Linear Algebra | Question: 6
Which of the following statements is/are $\textbf{NOT CORRECT}$? If $v1$ and $v2$ are linearly independent eigenvectors then they can correspond to the same eigenvalue. If $A$ is a nilpotent matrix, meaning that $A^k = 0$ for the ... is an eigenvalue of an invertible matrix $A$ then $\lambda ^{-1}$ is an eigenvalue of $A^{-1}$.
Which of the following statements is/are $\textbf{NOT CORRECT}$?If $v1$ and $v2$ are linearly independent eigenvectors then they can correspond to the same eigenvalue.If ...
GO Classes
70
views
GO Classes
asked
Apr 3
Linear Algebra
goclasses2025_csda_wq5
goclasses
linear-algebra
matrix
eigen-value
medium
multiple-selects
2-marks
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–
3
votes
1
answer
19
GO Classes CS/DA 2025 | Weekly Quiz 5 | Linear Algebra | Question: 3
Let the $n \times n$ matrix $A$ have an eigenvalue $\lambda$ with corresponding eigenvector $v$. Which of the following statements are true for matrix $A$. $-v$ is an eigenvector of $-A$ with eigenvalue $- \lambda$. If $v$ is also ... $A+B$. eigenvalue of $A^3$ is $\lambda^3$ and the eigenvector is $v^3$ .
Let the $n \times n$ matrix $A$ have an eigenvalue $\lambda$ with corresponding eigenvector $v$.Which of the following statements are true for matrix $A$.$-v$ is an eigen...
GO Classes
100
views
GO Classes
asked
Apr 3
Linear Algebra
goclasses2025_csda_wq5
goclasses
linear-algebra
matrix
eigen-value
medium
multiple-selects
2-marks
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–
3
votes
1
answer
20
GO Classes CS/DA 2025 | Weekly Quiz 5 | Linear Algebra | Question: 8
Which of the following statements is/are $\textbf{FALSE}$? For $n \times n$ real-symmetric matrices $A$ and $B$, $AB$ and $BA$ always have the same eigenvalues. For $n \times n$ matrices $A$ and $B$ with $B$ ... eigenvectors. For $n \times n$ real-symmetric matrices $A$ and $B$, $AB$ and $BA$ always have the same eigenvectors.
Which of the following statements is/are $\textbf{FALSE}$?For $n \times n$ real-symmetric matrices $A$ and $B$, $AB$ and $BA$ always have the same eigenvalues.For $n \tim...
GO Classes
78
views
GO Classes
asked
Apr 3
Linear Algebra
goclasses2025_csda_wq5
goclasses
linear-algebra
matrix
eigen-value
medium
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