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Recent questions tagged eigenvalues
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GATE201335
A matrix has eigenvalues $1$ and $2$. The corresponding eigenvectors are $\begin{vmatrix} 1\\1 \end{vmatrix}$ and $\begin{vmatrix} 1\\2 \end{vmatrix}$ respectively. The matrix is $\begin{vmatrix} 1 & 1\\ 1 & 2 \end{vmatrix}$ ... $\begin{vmatrix} 1 & 0\\ 0 & 2 \end{vmatrix}$ $\begin{vmatrix} 0& 1\\ 2 & 3 \end{vmatrix}$
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Feb 12, 2017
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piyag476
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gate2013ee
eigenvalues
eigenmatrix
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1
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2
GATE201421
Which one of the following statements is true for all real symmetric matrices? All the eigenvalues are real. All the eigenvalues are positive. All the eigenvalues are distinct. Sum of all the eigenvalues is zero.
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Feb 12, 2017
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Linear Algebra
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makhdoom ghaya
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9.2k
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gate2014ee2
eigenvalues
eigenmatrix
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3
GATE2014146
A system matrix is given as follows. $A=\begin{bmatrix} 0 & 1 & 1\\ 6 & 11 &6 \\ 6& 11& 5 \end{bmatrix}$ The absolute value of the ratio of the maximum eigenvalue to the minimum eigenvalue is _______
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Feb 12, 2017
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Linear Algebra
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makhdoom ghaya
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9.2k
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gate2014ee1
eigenvalues
eigenmatrix
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0
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4
GATE2015126
The maximum value of "a" such that the matrix $\begin{pmatrix} 3&0&2 \\ 1&1&0 \\ 0&a&2 \end{pmatrix}$ has three linearly independent real eigenvectors is $\frac{2}{3\sqrt{3}}$ $\frac{1}{3\sqrt{3}}$ $\frac{1+2\sqrt{3}}{3\sqrt{3}}$ $\frac{1+\sqrt{3}}{3\sqrt{3}}$
asked
Feb 12, 2017
in
Linear Algebra
by
makhdoom ghaya
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9.2k
points)
gate2015ee1
eigenvalues
eigenmatrix
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5
GATE2016128
Let the eigenvalues of a $2 \times 2$ matrix $A$ be $1, 2$ with eigenvectors $x_{1}$ and $x_{2}$ respectively. Then the eigenvalues and eigenvectors of the matrix $A^{2}3A+4I$ would, respectively, be $2, 14; x_{1}, x_{2}$ $2, 14; x_{1}+ x_{2}, x_{1}  x_{2}$ $2, 0; x_{1}, x_{2}$ $2, 0; x_{1}+ x_{2}, x_{1}  x_{2}$
asked
Jan 30, 2017
in
Linear Algebra
by
makhdoom ghaya
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9.2k
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gate2016ee1
eigenmatrix
eigenvalues
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