Recent questions tagged eigen-values - GO Electrical

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GATE2013-35
A matrix has eigenvalues $-1$ and $-2$. The corresponding eigenvectors are $\begin{bmatrix} 1\\-1 \end{bmatrix}$ and $\begin{bmatrix} 1\\-2 \end{bmatrix}$ respectibely. The matrix is $\begin{bmatrix} 1 & 1\\ -1 & -2 \end{bmatrix}$ ... $\begin{bmatrix} -1 & 0\\ 0 & -2 \end{bmatrix}$ $\begin{bmatrix} 0& 1\\ -2 & 3 \end{bmatrix}$

asked Feb 12, 2017 in Others by piyag476 (1.5k points)

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GATE2014-2-1
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.

asked Feb 12, 2017 in Linear Algebra by makhdoom ghaya (9.3k points)

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GATE2014-1-46
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 _______

asked Feb 12, 2017 in Linear Algebra by makhdoom ghaya (9.3k points)

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4

GATE2015-1-26
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 (9.3k points)

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GATE2016-1-28
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 (9.3k points)

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