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Recent questions tagged eigen-values
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GATE Mechanical 2021 Set 2 | Question: 1
Consider an $n \times n$ matrix $\text{A}$ and a non-zero $n \times 1$ vector $p.$ Their product $Ap=\alpha ^{2}p$, where $\alpha \in \Re$ and $\alpha \notin \left \{ -1,0,1 \right \}$. Based on the given information, the eigen value of $A^{2}$ is: $\alpha$ $\alpha ^{2}$ $\surd{\alpha }$ $\alpha ^{4}$
go_editor
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Linear Algebra
Mar 1, 2021
by
go_editor
5.0k
points
gateme-2021-set2
linear-algebra
matrices
eigen-values
0
answers
0
votes
GATE Mechanical 2021 Set 1 | Question: 26
Consider a vector $\text{p}$ in $2$-dimensional space. Let its direction (counter-clockwise angle with the positive $\text{x}$-axis) be $\theta$. Let $\text{p}$ be an eigenvector of a $2\times2$ matrix $\text{A}$ ... ${p}'=\theta ,\left \| {p}' \right \|= \left \| p \right \|/\lambda$
gatecse
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Linear Algebra
Feb 22, 2021
by
gatecse
1.6k
points
gateme-2021-set1
linear-algebra
eigen-values
eigen-vectors
0
answers
0
votes
GATE2020-ME-2: 19
Let $\textbf{I}$ be a $100$ dimensional identity matrix and $\textbf{E}$ be the set of its distinct (no value appears more than once in $\textbf{E})$ real eigen values. The number of elements in $\textbf{E}$ is _________
go_editor
asked
in
Linear Algebra
Sep 18, 2020
by
go_editor
5.0k
points
gateme-2020-set2
numerical-answers
linear-algebra
eigen-values
1
answer
0
votes
GATE2019 ME-2: 1
In matrix equation $[A] \{X\}=\{R\}$, $[A] = \begin{bmatrix} 4 & 8 & 4 \\ 8 & 16 & -4 \\ 4 & -4 & 15 \end{bmatrix} \{X\} = \begin{Bmatrix} 2 \\ 1 \\ 4 \end{Bmatrix} \text{ and} \{ R \} = \begin{Bmatrix} 32 \\ 16 \\ 64 \end{Bmatrix}$ One of the eigen values of matrix $[A]$ is $4$ $8$ $15$ $16$
Arjun
asked
in
Linear Algebra
Feb 9, 2019
by
Arjun
27.4k
points
gateme-2019-set2
linear-algebra
matrices
eigen-values
1
answer
1
vote
GATE2019 ME-1: 1
Consider the matrix $P=\begin{bmatrix} 1 & 1 & 0 \\ 0 & 1 & 1 \\ 0 & 0 & 1 \end{bmatrix}$ The number of distinct eigenvalues $0$ $1$ $2$ $3$
Arjun
asked
in
Linear Algebra
Feb 9, 2019
by
Arjun
27.4k
points
gateme-2019-set1
linear-algebra
matrices
eigen-values
0
answers
0
votes
GATE ME 2012 | Question: 36
For the matrix $A = \begin{bmatrix} 5 & 3 \\ 1 & 3 \end{bmatrix}$, ONE of the normalized eigen vectors is given as $\begin{pmatrix} \dfrac{1}{2} \\ \dfrac{\sqrt{3}}{2} \end{pmatrix} \\$ ... $\begin{pmatrix} \dfrac{1}{\sqrt{5}} \\ \dfrac{2}{\sqrt{5}} \end{pmatrix}$
Andrijana3306
asked
in
Linear Algebra
Mar 20, 2018
by
Andrijana3306
1.5k
points
gateme-2012
linear-algebra
eigen-values
eigen-vectors
1
answer
0
votes
GATE2017 ME-2: 28
Consider the matrix $A=\begin{bmatrix} 50 &70 \\ 70 & 80 \end{bmatrix}$ whose eigenvectors corresponding to eigenvalues $\lambda _{1}$ and $\lambda _{2}$ are $x_{1}=\begin{bmatrix} 70 \\ \lambda_{1}-50 \end{bmatrix}$ and $x_{2}=\begin{bmatrix} \lambda _{2}-80\\ 70 \end{bmatrix}$, respectively. The value of $x^{T}_{1} x_{2}$ is _________.
Arjun
asked
in
Linear Algebra
Feb 27, 2017
by
Arjun
27.4k
points
gateme-2017-set2
numerical-answers
linear-algebra
eigen-values
eigen-vectors
1
answer
0
votes
GATE2017 ME-2: 3
The determinant of a $2 \times 2$ matrix is $50$. If one eigenvalue of the matrix is $10$, the other eigenvalue is _________.
Arjun
asked
in
Linear Algebra
Feb 27, 2017
by
Arjun
27.4k
points
gateme-2017-set2
numerical-answers
linear-algebra
matrices
eigen-values
0
answers
0
votes
GATE2017 ME-1: 26
Consider the matrix $P=\begin{bmatrix} \dfrac{1}{\sqrt{2}} & 0 &\dfrac{1}{\sqrt{2}} \\ 0 & 1 & 0\\ -\dfrac{1}{\sqrt{2}} &0 & \dfrac{1}{\sqrt{2}} \end{bmatrix}$ Which one of the following statements about $P$ is INCORRECT ? Determinant of P is equal to $1$. $P$ is orthogonal. Inverse of $P$ is equal to its transpose. All eigenvalues of $P$ are real numbers.
Arjun
asked
in
Linear Algebra
Feb 27, 2017
by
Arjun
27.4k
points
gateme-2017-set1
linear-algebra
matrices
eigen-values
0
answers
0
votes
GATE2017 ME-1: 1
The product of eigenvalues of the matrix $P$ is $P=\begin{bmatrix} 2 & 0 & 1\\ 4& -3 &3 \\ 0 & 2 & -1 \end{bmatrix}$ $-6$ $2$ $6$ $-2$
Arjun
asked
in
Linear Algebra
Feb 27, 2017
by
Arjun
27.4k
points
gateme-2017-set1
linear-algebra
matrices
eigen-values
0
answers
0
votes
GATE2016-3-26
The number of linearly independent eigenvectors of matrix $A=\begin{bmatrix} 2 & 1 & 0\\ 0 &2 &0 \\ 0 & 0 & 3 \end{bmatrix}$ is _________
Arjun
asked
in
Linear Algebra
Feb 24, 2017
by
Arjun
27.4k
points
gateme-2016-set3
numerical-answers
linear-algebra
eigen-values
eigen-vectors
0
answers
0
votes
GATE2016-2-1
The condition for which the eigenvalues of the matrix $A=\begin{bmatrix} 2 & 1\\ 1 & k \end{bmatrix}$ are positive, is $k > 1/2$ $k > −2$ $k > 0$ $k < −1/2$
Arjun
asked
in
Linear Algebra
Feb 24, 2017
by
Arjun
27.4k
points
gateme-2016-set2
linear-algebra
matrices
eigen-values
0
answers
0
votes
GATE2015-2-1
At least one eigenvalue of a singular matrix is positive zero negative imaginary
Arjun
asked
in
Linear Algebra
Feb 24, 2017
by
Arjun
27.4k
points
gateme-2015-set2
linear-algebra
matrices
eigen-values
0
answers
0
votes
GATE Mechanical 2014 Set 3 | Question: 1
Consider a $3×3$ real symmetric matrix S such that two of its eigenvalues are $a\neq 0$, $b\neq 0$ with respective eigenvectors $\begin{bmatrix} x_1\\ x_2\\ x_3 \end{bmatrix}$, $\begin{bmatrix} y_1\\ y_2\\ y_3 \end{bmatrix}$ If $a\neq b$ then $x_1y_1+x_2y_2+x_3y_3$ equals $a$ $b$ $ab$ $0$
Arjun
asked
in
Linear Algebra
Feb 19, 2017
by
Arjun
27.4k
points
gateme-2014-set3
linear-algebra
matrices
eigen-values
eigen-vectors
0
answers
0
votes
GATE Mechanical 2014 Set 2 | Question: 1
One of the eigen vectors of the matrix $\begin{bmatrix} -5 & 2\\ -9 & 6 \end{bmatrix}$ is $\begin{Bmatrix} -1\\ 1 \end{Bmatrix} \\$ $\begin{Bmatrix} -2\\ 9 \end{Bmatrix} \\$ $\begin{Bmatrix} 2\\ -1 \end{Bmatrix} \\$ $\begin{Bmatrix} 1\\ 1 \end{Bmatrix} \\$
Arjun
asked
in
Linear Algebra
Feb 19, 2017
by
Arjun
27.4k
points
gateme-2014-set2
linear-algebra
eigen-values
eigen-vectors
0
answers
0
votes
GATE ME 2013 | Question: 2
The eigen values of a symmetric matrix are all complex with non-zero positive imaginary part. complex with non-zero negative imaginary part. real. pure imaginary.
piyag476
asked
in
Linear Algebra
Feb 19, 2017
by
piyag476
1.4k
points
gateme-2013
linear-algebra
matrices
eigen-values
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