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Recent questions tagged eigen-vectors
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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 $\text{A}$ ... ${p}'=\theta ,\left \| {p}' \right \|= \left \| p \right \|/\lambda$
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 ei...
gatecse
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gatecse
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Feb 22, 2021
Linear Algebra
gateme-2021-set1
linear-algebra
eigen-values
eigen-vectors
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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 $\begin{pmatrix} \dfrac{1}{2} \\ \dfrac{\sqrt{3}}{2} \end{pmatrix} \\$ ... $\begin{pmatrix} \dfrac{1}{\sqrt{5}} \\ \dfrac{2}{\sqrt{5}} \end{pmatrix}$
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} \en...
Andrijana3306
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Andrijana3306
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Mar 19, 2018
Linear Algebra
gateme-2012
linear-algebra
eigen-values
eigen-vectors
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1
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0
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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 _________.
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{b...
Arjun
28.5k
points
Arjun
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Feb 26, 2017
Linear Algebra
gateme-2017-set2
numerical-answers
linear-algebra
eigen-values
eigen-vectors
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0
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0
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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 _________
The number of linearly independent eigenvectors of matrix $A=\begin{bmatrix} 2 & 1 & 0\\ 0 &2 &0 \\ 0 & 0 & 3 \end{bmatrix}$ is _________
Arjun
28.5k
points
Arjun
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Feb 24, 2017
Linear Algebra
gateme-2016-set3
numerical-answers
linear-algebra
eigen-values
eigen-vectors
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0
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0
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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 $a$ $b$ $ab$ $0$
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{bma...
Arjun
28.5k
points
Arjun
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Feb 19, 2017
Linear Algebra
gateme-2014-set3
linear-algebra
matrices
eigen-values
eigen-vectors
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0
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0
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GATE Mechanical 2014 Set 2 | Question: 1
One of the eigen vectors of the matrix $\begin{bmatrix} -5 & 2\\ -9 & 6 \end{bmatrix}$ is $\begin{Bmatrix} -1\\ 1 \end{Bmatrix} \\$ $\begin{Bmatrix} -2\\ 9 \end{Bmatrix} \\$ $\begin{Bmatrix} 2\\ -1 \end{Bmatrix} \\$ $\begin{Bmatrix} 1\\ 1 \end{Bmatrix} \\$
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} \\...
Arjun
28.5k
points
Arjun
asked
Feb 19, 2017
Linear Algebra
gateme-2014-set2
linear-algebra
eigen-values
eigen-vectors
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