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Recent questions tagged eigen-values
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GATE ECE 2021 | Question: 36
A real $2\times2$ non-singular matrix $A$ with repeated eigenvalue is given as $A=\begin{bmatrix} x & -3.0\\ 3.0 & 4.0 \end{bmatrix}$ where $x$ is a real positive number. The value of $x$ (rounded off to one decimal place) is ________________
Arjun
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Linear Algebra
Feb 20, 2021
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Arjun
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gateec-2021
numerical-answers
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2
GATE ECE 2019 | Question: 17
The number of distinct eigenvalues of the matrix $A=\begin{bmatrix} 2&2&3&3\\0&1&1&1\\0&0&3&3\\0&0&0&2 \end{bmatrix}$ is equal to ____________.
Arjun
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Linear Algebra
Feb 12, 2019
by
Arjun
4.5k
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96
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gate2019-ec
numerical-answers
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3
GATE ECE 2016 Set 2 | Question: 1
The value of $x$ for which the matrix $A= \begin{bmatrix} 3& 2 &4 \\ 9& 7 & 13\\ -6&-4 &-9+x \end{bmatrix}$ has zero as an eigenvalue is ________
Milicevic3306
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Linear Algebra
Mar 28, 2018
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Milicevic3306
15.8k
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39
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gate2016-ec-2
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4
GATE ECE 2015 Set 2 | Question: 2
The value of $x$ for which all the eigen-values of the matrix given below are real is $\begin{bmatrix} 10&5+j &4 \\ x&20 &2 \\4 &2 &-10 \end{bmatrix}$ $5+j$ $5-j$ $1-5j$ $1+5j$
Milicevic3306
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Linear Algebra
Mar 28, 2018
by
Milicevic3306
15.8k
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41
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gate2015-ec-2
linear-algebra
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5
GATE ECE 2015 Set 1 | Question: 5
The value of $p$ such that the vector $\begin{bmatrix} 1 \\ 2 \\ 3 \end{bmatrix}$ is an eigenvector of the matrix $\begin{bmatrix} 4 & 1 & 2 \\ p & 2 & 1 \\ 14 & -4 & 10 \end{bmatrix}$ is _________.
Milicevic3306
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Linear Algebra
Mar 28, 2018
by
Milicevic3306
15.8k
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28
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gate2015-ec-1
numerical-answers
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6
GATE ECE 2014 Set 3 | Question: 27
Which one of the following statements is NOT true for a square matrix $A$? If $A$ is upper triangular, the eigenvalues of $A$ are the diagonal elements of it If $A$ is real symmetric, the eigenvalues of $A$ are always real and positive If $A$ ... $A$ are positive, all the eigenvalues of $A$ are also positive
Milicevic3306
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Linear Algebra
Mar 26, 2018
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Milicevic3306
15.8k
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47
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gate2014-ec-3
linear-algebra
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0
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7
GATE ECE 2014 Set 1 | Question: 4
A real $(4 \times 4)$ matrix $A$ satisfies the equation $A^{2} = I$, where $I$ is the $(4 \times 4)$ identity matrix. The positive eigen value of $A$ is ______.
Milicevic3306
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Linear Algebra
Mar 26, 2018
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Milicevic3306
15.8k
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58
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gate2014-ec-1
linear-algebra
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numerical-answers
0
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1
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8
GATE ECE 2013 | Question: 19
The minimum eigenvalue of the following matrix is $\begin{bmatrix} 3& 5& 2\\5 &12 &7 \\2 &7 & 5\end{bmatrix}$ $0$ $1$ $2$ $3$
Milicevic3306
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Linear Algebra
Mar 26, 2018
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Milicevic3306
15.8k
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441
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gate2013-ec
linear-algebra
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9
GATE ECE 2018 | Question: 11
Let $\text{M}$ be a real $4\times 4$ matrix. Consider the following statements: $S1: M $ has $4$ linearly independent eigenvectors. $S2: M$ has $4$ distinct eigenvalues. $S3: M$ is non-singular (invertible). Which one among the following is TRUE? $S1$ implies $S2$ $S1$ implies $S3$ $S2$ implies $S1$ $S3$ implies $S2$
gatecse
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Linear Algebra
Feb 19, 2018
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gatecse
1.5k
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51
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gate2018-ec
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0
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10
GATE ECE 2017 Set 1 | Question: 1
Consider the 5 $\times$ 5 matrix $\begin{bmatrix} 1&2&3&4&5\\ 5&1 &2& 3 &4\\ 4&5&1&2&3\\ 3&4&5&1&2\\ 2&3&4&5&1 \end{bmatrix}$ It is given that A has only one real eigenvalue. Then the real eigenvalue of A is $-2.5$ $0$ $15$ $25$
admin
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Linear Algebra
Nov 17, 2017
by
admin
2.8k
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302
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gate2017-ec-1
linear-algebra
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