GATE2016-3-1

Arjun asked in Linear Algebra Feb 24, 2017 recategorized Mar 5, 2021 by Lakshman Patel RJIT

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A real square matrix $\textbf{A}$ is called skew-symmetric if

$A^T=A$
$A^T=A^{-1}$
$A^T=-A$
$A^T=A+A^{-1}$

gateme-2016-set3
linear-algebra
matrices

Arjun asked in Linear Algebra Feb 24, 2017 recategorized Mar 5, 2021 by Lakshman Patel RJIT

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Arjun asked in Linear Algebra Feb 24, 2017

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

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gateme-2016-set2
linear-algebra
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Arjun asked in Linear Algebra Feb 24, 2017

GATE2016-1-1
The solution to the system of equations $\begin{bmatrix} 2 & 5\\-4 &3 \end{bmatrix}\begin{bmatrix} x\\y \end{bmatrix}=\begin{bmatrix} 2\\ -30 \end{bmatrix}$ is $6,2$ $-6,2$ $-6,-2$ $6,-2$

Arjun asked in Linear Algebra Feb 24, 2017

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gateme-2016-set1
linear-algebra
matrices
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Arjun asked in Linear Algebra Feb 19, 2017

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

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gateme-2014-set3
linear-algebra
matrices
eigen-values
eigen-vectors

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Arjun asked in Linear Algebra Feb 24, 2017

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

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gateme-2016-set3
numerical-answers
linear-algebra
eigen-values
eigen-vectors

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Arjun asked in Linear Algebra Feb 27, 2017

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

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27.4k points

gateme-2017-set2
numerical-answers
linear-algebra
matrices
eigen-values

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GATE2016-3-1

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