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Recent questions tagged linearalgebra
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GATE2019 EC: 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 ____________.
asked
Feb 12, 2019
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Arjun
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gate2019ec
numericalanswers
matrixalgebra
linearalgebra
engineeringmathematics
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0
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2
GATE2019 EC: 20
Let $Z$ be an exponential random variable with mean $1$. That is, the cumulative distribution function of $Z$ is given by $F_{Z}(x)= \left\{\begin{matrix} 1e^{x}& \text{if}\: x \geq 0 \\ 0& \text{if}\: x< 0 \end{matrix}\right.$ Then $Pr\left(Z>2 \mid Z>1\right),$ rounded off to two decimal places, is equal to ___________.
asked
Feb 12, 2019
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Arjun
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gate2019ec
numericalanswers
engineeringmathematics
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linearalgebra
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3
GATE201631
Consider a $2\times2$ sqaure matrix $\textbf{A}= \begin{bmatrix} \sigma &x\\ \omega &\sigma \end{bmatrix},$ where $x$ is unknown. If the eigen values of the matrix $\textbf{A}$ are $(\sigma + j\omega)$ and $(\sigma  j\omega)$, then $x$ is equal to $+j\omega$ $j\omega$ $+\omega$ $\omega$
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Mar 28, 2018
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gate2016ec3
matrixalgebra
linearalgebra
engineeringmathematics
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0
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4
GATE2016334
The $z$parameter matrix $\begin{bmatrix} z_{11} &z_{12}\\ z_{21} &z_{22} \end{bmatrix}$ for the twoport network shown is $\begin{bmatrix} 2 &2\\2 &2 \end{bmatrix} \\$ $\begin{bmatrix} 2 &2\\2 &2 \end{bmatrix} \\$ $\begin{bmatrix} 9 &3\\6 &9 \end{bmatrix} \\$ $\begin{bmatrix} 9 &3\\6 &9 \end{bmatrix}$
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Mar 28, 2018
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Milicevic3306
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15.7k
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gate2016ec3
matrixalgebra
linearalgebra
engineeringmathematics
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0
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5
GATE201621
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 ________
asked
Mar 28, 2018
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Milicevic3306
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15.7k
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gate2016ec2
numericalanswers
matrixalgebra
linearalgebra
engineeringmathematics
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0
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6
GATE201629
The $z$parameter matrix for the twoport network shown is $\begin{bmatrix} 2j\omega &j\omega \\ j\omega & 3+2j\omega \end{bmatrix},$ where the entries are in $\Omega$. Suppose $Z_{b}\left ( j\omega \right )=R_{b}+j\omega .$ Then the value of $R_{b}$ (in $\Omega$) equals ________
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Mar 28, 2018
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gate2016ec2
numericalanswers
matrixalgebra
linearalgebra
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7
GATE2016229
The matrix $A=\begin{bmatrix} a & 0 &3 &7 \\ 2& 5&1 &3 \\ 0& 0& 2 &4 \\ 0&0 & 0 &b \end{bmatrix}$ has $\text{det}(A) = 100$ and $\text{trace}(A) = 14$. The value of $\mid ab \mid$ is ________
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Mar 28, 2018
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Milicevic3306
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15.7k
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gate2016ec2
numericalanswers
matrixalgebra
linearalgebra
engineeringmathematics
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0
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8
GATE201616
Which one of the following is an eigen function of the class of all continuoustime, linear, timeinvariant systems ($u(t)$ denotes the unitstep function)? $e^{j\omega_0t}u(t)$ $\cos(\omega_0t)$ $e^{j\omega_0t}$ $\sin(\omega_0t)$
asked
Mar 28, 2018
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15.7k
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gate2016ec1
linearalgebra
eigenvalues
engineeringmathematics
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0
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9
GATE2016127
A sequence $x[n]$ is specified as $\begin{bmatrix}x[n] \\x[n – 1]\end{bmatrix}=\begin{bmatrix}1&1\\1&0\end{bmatrix}^n\begin{bmatrix}1\\0\end{bmatrix}$,for $n \geq 2$. The initial conditions are $x[0] = 1$, $x[1] = 1$, and $x[n] = 0$ for $n < 0$. The value of $x[12]$ is _________
asked
Mar 28, 2018
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by
Milicevic3306
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15.7k
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gate2016ec1
numericalanswers
linearalgebra
engineeringmathematics
matrix
+1
vote
0
answers
10
GATE201531
For $A = \begin{bmatrix} 1 &\tan x \\ \tan x &1 \end{bmatrix},$ the determinant of $A^{T}A^{1}$ is $\sec^{2}x$ $\cos 4x$ $1$ $0$
asked
Mar 28, 2018
in
Linear Algebra
by
Milicevic3306
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15.7k
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gate2015ec3
linearalgebra
matrix
0
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0
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11
GATE201522
The value of $x$ for which all the eigenvalues of the matrix given below are real is $\begin{bmatrix} 10&5+j &4 \\ x&20 &2 \\4 &2 &10 \end{bmatrix}$ $5+j$ $5j$ $15j$ $1+5j$
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Mar 28, 2018
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by
Milicevic3306
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15.7k
points)
gate2015ec2
linearalgebra
engineeringmathematics
eigenvalues
0
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0
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12
GATE201528
The $2$port admittance matrix of the circuit shown is given by $\begin{bmatrix}0.3 &0.2 \\0.2 &0.3 \end{bmatrix}$ $\begin{bmatrix} 15&5 \\5 &15 \end{bmatrix}$ $\begin{bmatrix} 3.33&5 \\5 &3.33 \end{bmatrix}$ $\begin{bmatrix} 0.3&0.4 \\0.4 &0.3 \end{bmatrix}$
asked
Mar 28, 2018
in
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by
Milicevic3306
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15.7k
points)
gate2015ec2
linearalgebra
engineeringmathematics
matrix
0
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0
answers
13
GATE2015246
The state variable representation of a system is given as $\dot{x} = \begin{bmatrix} 0 &1 \\ 0 &1 \end{bmatrix}\: ; x(0)=\begin{bmatrix} 1\\0 \end{bmatrix}$ $y=\begin{bmatrix} 0 &1 \end{bmatrix} x$ The response $y(t)$ is $\sin(t)$ $1e^{t}$ $1\cos(t)$ $0$
asked
Mar 28, 2018
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by
Milicevic3306
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15.7k
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gate2015ec2
matrixalgebra
linearalgebra
engineeringmathematics
0
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0
answers
14
GATE2015250
$\begin{Bmatrix} X_{n}\\ \end{Bmatrix}_{n=\infty}^{n=\infty}$ is an independent and identically distributed (i.i.d.) random process with ܺ$X_{n}$ equally likely to be $+1$ or $−1.\:\:\begin{Bmatrix} Y_{n}\\ \end{Bmatrix}_{n=\infty}^{n=\infty}$ is another ... $\begin{Bmatrix} Y_{n}\\ \end{Bmatrix}_{n=\infty}^{n=\infty},$ denoted by $R_{Y}[k],$ is
asked
Mar 28, 2018
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Milicevic3306
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15.7k
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gate2015ec2
linearalgebra
engineeringmathematics
matrixalgebra
0
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0
answers
15
GATE201511
Consider a system of linear equations: $x2y+3z=1, \\ x3y+4z=1, \text{ and } \\ 2x+4y6z=k.$ The value of $k$ for which the system has infinitely many solutions is ___________
asked
Mar 28, 2018
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Others
by
Milicevic3306
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15.7k
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gate2015ec1
numericalanswers
linearalgebra
engineeringmathematics
0
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0
answers
16
GATE201515
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 _________.
asked
Mar 28, 2018
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Milicevic3306
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15.7k
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gate2015ec1
numericalanswers
linearalgebra
engineeringmathematics
matrix
0
votes
0
answers
17
GATE2014347
The state equation of a secondorder linear system is given by $\dot{x}(t)=Ax(t), \:\:\:\:\:\:\:\:x(0)=x_{0}$ For $x_{0}= \begin{bmatrix} 1\\ 1 \end{bmatrix},$ $x(t)= \begin{bmatrix} e^{t}\\ e^{t} \end{bmatrix},$ ... $\begin{bmatrix} 5e^{t}3e^{2t}\\ 5e^{t}+6e^{2t} \end{bmatrix}$
asked
Mar 26, 2018
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Milicevic3306
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15.7k
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gate2014ec3
linearalgebra
networksolutionmethods
steadystate
networks
0
votes
0
answers
18
GATE201421
The determinant of matrix $A$ is $5$ and the determinant of matrix B is $40$. The determinant of matrix $AB$ is ________
asked
Mar 26, 2018
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Milicevic3306
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15.7k
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gate2014ec2
numericalanswers
matrix
linearalgebra
engineeringmathematics
0
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0
answers
19
GATE2014226
The system of linear equations $\begin{pmatrix} 2 & 1 & 3\\ 3&0 &1 \\ 1& 2 &5 \end{pmatrix} \begin{pmatrix} a\\ b\\ c \end{pmatrix} = \begin{pmatrix} 5\\ 4\\ 14 \end{pmatrix}$ has a unique solution infinitely many solutions no solution exactly two solutions
asked
Mar 26, 2018
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by
Milicevic3306
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15.7k
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gate2014ec2
linearalgebra
matrix
0
votes
0
answers
20
GATE201414
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 ______.
asked
Mar 26, 2018
in
Linear Algebra
by
Milicevic3306
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15.7k
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gate2014ec1
linearalgebra
matrix
eigenvalues
numericalanswers
0
votes
0
answers
21
GATE201355
The state diagram of a system is shown below. A system is described by the statevariable equations $\dot{X}= AX+Bu;\:\: y = CX+Du$ The state transition matrix $e^{At}$ of the system shown in the figure above is $\begin{bmatrix} e^{t}& 0\\te^{t} &e^{t} \end{bmatrix}$ ... $\begin{bmatrix} e^{t}&te^{t} \\ 0 &e^{t} \end{bmatrix}$
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Mar 26, 2018
in
Linear Algebra
by
Milicevic3306
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15.7k
points)
gate2013ec
linearalgebra
matrix
0
votes
0
answers
22
GATE201327
Let $A$ be an $m \times n$ matrix and $B$ an $n \times m$ matrix. It is given that determinant $(I_{m} + AB) =$ determinant $(I_{n} + BA),$ where $I_{k}$ is the $k \times k$ ... $2$ $5$ $8$ $16$
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Mar 26, 2018
in
Linear Algebra
by
Milicevic3306
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15.7k
points)
gate2013ec
linearalgebra
matrix
determinant
0
votes
1
answer
23
GATE201319
The minimum eigenvalue of the following matrix is $\begin{bmatrix} 3& 5& 2\\5 &12 &7 \\2 &7 & 5\end{bmatrix}$ $0$ $1$ $2$ $3$
asked
Mar 26, 2018
in
Linear Algebra
by
Milicevic3306
(
15.7k
points)
gate2013ec
linearalgebra
eigenvalues
0
votes
0
answers
24
GATE201247
Given that $A=\begin{bmatrix} 5 &3 \\ 2 &0\end{bmatrix}$ and $I=\begin{bmatrix} 1 & 0 \\ 0 &1\end{bmatrix}$, the value of $A^3$ is $15\:A+12\:I$ $19\:A+30\:I$ $17\:A+15\:I$ $17\:A+21\:I$
asked
Mar 25, 2018
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Milicevic3306
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15.7k
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gate2012ec
linearalgebra
engineeringmathematics
matrix
0
votes
0
answers
25
GATE201822
Consider matrix $A=\begin{bmatrix} k & 2k\\ k^{2}k & k^{2} \end{bmatrix}$ and vector $x=\begin{bmatrix} x_{1}\\ x_{2} \end{bmatrix}.$ The number of distinct real value of $k$ for which the equation $Ax=0$ has infinitely many solutions is _________.
asked
Feb 19, 2018
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gatecse
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1.4k
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gate2018ec
numericalanswers
matrixalgebra
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26
GATE201811
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 nonsingular (invertible). Which one among the following is TRUE? $S1$ implies $S2$ $S1$ implies $S3$ $S2$ implies $S1$ $S3$ implies $S2$
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Feb 19, 2018
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gatecse
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gate2018ec
matrix
linearalgebra
engineeringmathematics
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0
answers
27
GATE2017 EC2: 30
The minimum value of the function $f(x)=\frac{1}{3} x(x^23)$ in the interval $100≤x≤100$ occurs at $x =$ ________.
asked
Nov 23, 2017
in
Linear Algebra
by
admin
(
2.8k
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gate2017ec2
numericalanswers
linearalgebra
engineeringmathematics
0
votes
0
answers
28
GATE2017 EC2: 4
The residues of a function $f(z)=\frac1{(z4)(z+1)^3 }$ are $\frac{1}{27}$ and $\frac{1}{125} \\$ $\frac{1}{125}$ and $\frac{1}{125} \\$ $\frac{1}{27}$ and $\frac{1}{5} \\$ $\frac{1}{125}$and $\frac{1}{5}$
asked
Nov 23, 2017
in
Linear Algebra
by
admin
(
2.8k
points)
gate2017ec2
linearalgebra
0
votes
0
answers
29
GATE2017 EC2: 1
The rank of the matrix $\begin{bmatrix} 1 & 1& 0& 0& 0& \\ 0& 0& 1& 1& 0& \\ 0& 1& 1& 0& 0& \\ 1& 0& 0& 0& 1& \\ 0& 0& 0& 1& 1& \end{bmatrix}$ is ________.
asked
Nov 23, 2017
in
Linear Algebra
by
admin
(
2.8k
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gate2017ec2
matrixalgebra
rank
numericalanswers
linearalgebra
0
votes
0
answers
30
GATE2017 EC1: 48
Which one of the following options correctly describes the locations of the roots of the equation $s^{4}+s^{2}+1=0$ on the complex plane? Four left half plane(LHP) roots One right half plane(RHP) root,one LHP root and two roots on the imaginary axis Two RHP roots and two LHP roots All four roots are on the imaginary axis
asked
Nov 17, 2017
in
Linear Algebra
by
admin
(
2.8k
points)
gate2017ec1
linearalgebra
linearequations
0
votes
0
answers
31
GATE2017 EC1: 2
The rank of the matrix $\textbf{M} = \begin{bmatrix} 5&10&10 \\ 1 &0 &2 \\ 3&6&6 \end{bmatrix}$ is $0$ $1$ $2$ $3$
asked
Nov 17, 2017
in
Linear Algebra
by
admin
(
2.8k
points)
gate2017ec1
matrixalgebra
rank
linearalgebra
0
votes
0
answers
32
GATE2017 EC1: 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 $2.5$ $0$ $15$ $25$
asked
Nov 17, 2017
in
Linear Algebra
by
admin
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2.8k
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gate2017ec1
matrixalgebra
eigenvalues
linearalgebra
engineeringmathematics
0
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0
answers
33
GATE2017 EC1: 3
Consider the following statements about the linear dependence of the real valued function $y_{1}=1,y_{2}=x$ and $y_{3}=x^{2}$ over the field of real numbers. $y_{1},y_{2}$ and $y_{3} $ are linearly independent on $1\leq x\leq 0$ ... Which one among the following is correct? Both I and II are true Both I and III are true Both II and IV are true Both III and IV are true
asked
Nov 17, 2017
in
Linear Algebra
by
admin
(
2.8k
points)
gate2017ec1
linearequations
linearalgebra
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