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Recent questions and answers in Linear Algebra
0
votes
1
answer
1
GATE201319
The minimum eigenvalue of the following matrix is $\begin{bmatrix} 3& 5& 2\\5 &12 &7 \\2 &7 & 5\end{bmatrix}$ $0$ $1$ $2$ $3$
answered
Nov 26, 2019
in
Linear Algebra
by
Lakshman Patel RJIT
(
230
points)
gate2013ec
linearalgebra
eigenvalues
+1
vote
0
answers
2
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
(
15.7k
points)
gate2015ec3
linearalgebra
matrix
0
votes
0
answers
3
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
(
15.7k
points)
gate2014ec1
linearalgebra
matrix
eigenvalues
numericalanswers
0
votes
0
answers
4
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 $\begin{bmatrix} e^{t}& 0\\te^{t} &e^{t} \end{bmatrix}$ ... $\begin{bmatrix} e^{t}&te^{t} \\ 0 &e^{t} \end{bmatrix}$
asked
Mar 26, 2018
in
Linear Algebra
by
Milicevic3306
(
15.7k
points)
gate2013ec
linearalgebra
matrix
0
votes
0
answers
5
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 $k \times k$ ... $2$ $5$ $8$ $16$
asked
Mar 26, 2018
in
Linear Algebra
by
Milicevic3306
(
15.7k
points)
gate2013ec
linearalgebra
matrix
determinant
0
votes
0
answers
6
GATE2017 EC2: 28
If the vector function $\overrightarrow{F}=\widehat{a_x}(3yk_1z)+\widehat{a_y}(k_2x2z)\widehat{a_z}(k_3y+z)$ is irrotational, then the values of the constants $k_1$,$k_2$ and $k_3$, respectively, are $0.3, 2.5, 0.5$ $0.0, 3.0, 2.0$ $0.3, 0.33, 0.5$ $4.0, 3.0, 2.0$
asked
Nov 23, 2017
in
Linear Algebra
by
admin
(
2.8k
points)
gate2017ec2
vectoranalysis
overrightarrow
engineeringmathematics
0
votes
0
answers
7
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
points)
gate2017ec2
numericalanswers
linearalgebra
engineeringmathematics
0
votes
0
answers
8
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
9
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
points)
gate2017ec2
matrixalgebra
rank
numericalanswers
linearalgebra
0
votes
0
answers
10
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
11
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
(
2.8k
points)
gate2017ec1
matrixalgebra
eigenvalues
linearalgebra
engineeringmathematics
0
votes
0
answers
12
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
13
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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