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Recent questions and answers in Linear Algebra
0
votes
0
answers
1
Gate2006EE
...
asked
Sep 29, 2019
in
Linear Algebra
by
KUSHAGRA गुप्ता
(
120
points)
gate2006ee
linearalgebra
0
votes
1
answer
2
GATE201421
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.
answered
Oct 26, 2018
in
Linear Algebra
by
Abhisek Tiwari 4
(
140
points)
gate2014ee2
eigenvalues
eigenmatrix
+1
vote
0
answers
3
GATE201350
The state variable formulation of a system is given as ... The system is controllable but not observable not controllable but observable both controllable and observable both not controllable and not observable
asked
Feb 12, 2017
in
Linear Algebra
by
piyag476
(
1.5k
points)
gate2013ee
linearalgebra
stateequations
systemoflinearequations
0
votes
0
answers
4
GATE201351
The state variable formulation of a system is given as $\begin{bmatrix} x^\cdot_1 \\ x^\cdot_2 \end{bmatrix}=\begin{bmatrix} 2 & 0\\ 0 & 1 \end{bmatrix}\begin{bmatrix} x_1\\ x_2 \end{bmatrix}+\begin{bmatrix} 1\\ 1 \end{bmatrix}u$ , $x_1(0)=0$ , $x_2(0)=0$ ... $1\dfrac{1}{2}e^{2t}\dfrac{1}{2}e^{t} \\$ $e^{2t}e^{t} \\$ $1e^{t}$
asked
Feb 12, 2017
in
Linear Algebra
by
piyag476
(
1.5k
points)
gate2013ee
linearalgebra
stateequations
systemoflinearequations
0
votes
0
answers
5
GATE201325
The equation$\begin{bmatrix} 2&2 \\ 1& 1 \end{bmatrix}\begin{bmatrix} x_1\\ x_2 \end{bmatrix}=\begin{bmatrix} 0\\0 \end{bmatrix}$ has no solution only one solution $\begin{bmatrix} x1\\x2 \end{bmatrix}=\begin{bmatrix} 0\\0 \end{bmatrix}$ nonzero unique solution multiple solutions
asked
Feb 12, 2017
in
Linear Algebra
by
piyag476
(
1.5k
points)
gate2013ee
linearalgebra
matrix
systemoflinearequations
0
votes
0
answers
6
GATE201431
Two matrices $A$ and $B$ are given below: $A=\begin{vmatrix} p & q\\ r & s \end{vmatrix}$; $B=\begin{vmatrix} p^2+q^2 & pr+qs\\ pr+qs &r^2+s^2 \end{vmatrix}$ If the rank of matrix $A$ is $N$, then the rank of matrix $B$ is $N/2$ $N – 1$ $N$ $2N$
asked
Feb 12, 2017
in
Linear Algebra
by
makhdoom ghaya
(
9.3k
points)
gate2014ee3
matrix
rank
0
votes
0
answers
7
GATE20143GA8
The Gross Domestic Product $(GDP)$ in Rupees grew at $7\%$ during $2012$$2013$.For international comparison, the $GDP$ is compared in $US$ Dollars $(USD)$ after conversion based on the market exchange rate. During the period $20122013$ ... $20122013$ increased by $5 \%$ decreased by $13\%$ decreased by $20\%$ decreased by $11\%$
asked
Feb 12, 2017
in
Linear Algebra
by
makhdoom ghaya
(
9.3k
points)
gate2014ee3
grossdomesticproduct
marketexchangerate
0
votes
0
answers
8
GATE20142GA8
If x is real and $x^2 − 2x + 3$ = $11$, then possible values of $ x^3 + x^2 − x$ include $2,4$ $2,14$ $4,52$ $14,52$
asked
Feb 12, 2017
in
Linear Algebra
by
makhdoom ghaya
(
9.3k
points)
gate2014ee2
algebra
matrix
0
votes
0
answers
9
GATE2014146
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)
gate2014ee1
linearalgebra
eigenvalues
eigenmatrix
numericalanswers
0
votes
0
answers
10
GATE201411
Given a system of equations: $x+2y+2z=b_1$ $5x+y+3z=b_2$ Which of the following is true regarding its solutions The system has a unique solution for any given $b_1$ and $b_2$ The system will have infinitely many solutions for any given $b_1$ and $b_2$ Whether ... a solution exists depends on the given $b_1$ and $b_2$ The system would have no solution for any values of $b_1$ and $b_2$
asked
Feb 12, 2017
in
Linear Algebra
by
makhdoom ghaya
(
9.3k
points)
gate2014ee1
linearequation
matrix
systemoflinearequations
0
votes
0
answers
11
GATE20141GA4
If $(z+1/z)^2 = 98,$ compute $(z^2+1/z^2).$
asked
Feb 12, 2017
in
Linear Algebra
by
makhdoom ghaya
(
9.3k
points)
gate2014ee1
complexnumber
numericalanswers
0
votes
0
answers
12
GATE201523
Match the following. P. Stokes’s Theorem 1. $∯ D.ds = Q$ Q. Gauss’s Theorem 2. $\oint f(z) dz =0$ R. Divergence Theorem 3. $\int \int \int (\triangledown. A) dv = ∯ A. ds$ S. Cauchy’s Integral Theorem 4. $\int \int (\triangledown \times A).ds = \oint A. dl$ (A) P2 Q1 R4 S3 (B) P4 Q1 R3 S2 (C) P4 Q3 R1 S2 (D) P3 Q4 R2 S1
asked
Feb 12, 2017
in
Linear Algebra
by
makhdoom ghaya
(
9.3k
points)
gate2015ee2
gausselimination
integraltheorem
0
votes
0
answers
13
GATE201522
We have a set of $3$ linear equations in $3$ unknowns. $'X \equiv Y'$ means $X$ and $Y$ are equivalent statements and $'X \not\equiv Y'$ means $X$ and $Y$ are not equivalent statements. P: There is a unique solution. Q: The equations are linearly independent. R: All ... $P \equiv Q \not\equiv R \equiv S$ $P\not\equiv Q \not\equiv R \not\equiv S$
asked
Feb 12, 2017
in
Linear Algebra
by
makhdoom ghaya
(
9.3k
points)
gate2015ee2
linearequations
eigenvalues
0
votes
0
answers
14
GATE20152GA8
If $p, q, r, s$ are distinct integers such that: $f(p, q, r, s) = \max (p, q, r, s)$ $g(p, q, r, s) = \min (p, q, r, s)$ $h(p, q, r, s)$ = remainder of $(p \times q) / (r \times s)$ if $(p \times q) > (r \times s)$ or remainder of ... $f(p, q)$. What is the value of $fg (h (2, 5, 7, 3), 4, 6, 8)$ ?
asked
Feb 12, 2017
in
Linear Algebra
by
makhdoom ghaya
(
9.3k
points)
gate2015ee2
remainder
operator
num
numericalanswers
0
votes
0
answers
15
GATE2015126
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 $\dfrac{2}{3\sqrt{3}} \\$ $\dfrac{1}{3\sqrt{3}} \\$ $\dfrac{1+2\sqrt{3}}{3\sqrt{3}} \\$ $\dfrac{1+\sqrt{3}}{3\sqrt{3}}$
asked
Feb 12, 2017
in
Linear Algebra
by
makhdoom ghaya
(
9.3k
points)
gate2015ee1
eigenvalues
eigenmatrix
0
votes
0
answers
16
GATE2016249
Consider a linear time invariant system $\dot{x}=Ax$ with initial condition $x(0)$ at $t=0$. Suppose $\alpha$ and $\beta$ are eigenvectors of $(2 \times 2)$ matrix $A$ corresponding to distinct eigenvalues $\lambda_{1}$ and $\lambda_{2}$ respectively. Then the response $x(t)$ ... $e^{\lambda_{2}t}\beta$ $e^{\lambda_{2}t}\alpha$ $e^{\lambda_{1}t}\alpha+e^{\lambda_{2}t}\beta$
asked
Jan 30, 2017
in
Linear Algebra
by
makhdoom ghaya
(
9.3k
points)
gate2016ee2
lineartimeinvariantsystem
eigenvalues
0
votes
0
answers
17
GATE2016232
Let $P=\begin{bmatrix} 3&1 \\ 1 & 3 \end{bmatrix}$ Consider the set $S$ of all vectors $\begin{pmatrix} x\\ y \end{pmatrix}$ such that $a^{2}+b^{2}=1$ ... An ellipse with major axis along $\begin{pmatrix} 1\\ 1 \end{pmatrix}$ An ellipse with minor axis along $\begin{pmatrix} 1\\ 1 \end{pmatrix}$
asked
Jan 30, 2017
in
Linear Algebra
by
makhdoom ghaya
(
9.3k
points)
gate2016ee2
circleequations
vectors
0
votes
0
answers
18
GATE201627
A $3 \times 3$ matrix $P$ is such that, $P^{3}=P$. Then the eigenvalues of $P$ ܲ are $1, 1, −1$ $1, 0.5 + ݆j0.866, 0.5 − ݆j0.866$ $1,−0.5 + ݆j0.866, −0.5 − ݆j0.866$ $0, 1, −1$
asked
Jan 30, 2017
in
Linear Algebra
by
makhdoom ghaya
(
9.3k
points)
gate2016ee2
eigenspace
nontrivialsolution
determinant
0
votes
0
answers
19
GATE20161GA5
In a quadratic function, the value of the product of the roots $(\alpha, \beta)$ is $4$. Find the value of $\frac{\alpha^{n}+\beta^{n}}{\alpha^{n}+\beta^{n}}$ $n^{4}$ $4^{n}$ $2^{2n1}$ $4^{n1}$
asked
Jan 30, 2017
in
Linear Algebra
by
makhdoom ghaya
(
9.3k
points)
gate2016ee1
functions
roots
sequence
0
votes
0
answers
20
GATE2016133
Given the following polynomial equation $s^{3}+5.5 s^{2}+8.5s+3=0$ the number of roots of the polynomial, which have real parts strictly less than $−1$, is ________.
asked
Jan 30, 2017
in
Linear Algebra
by
makhdoom ghaya
(
9.3k
points)
gate2016ee1
multiplicity
degreeofpolynomial
numericalanswers
0
votes
0
answers
21
GATE2016128
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)
gate2016ee1
eigenmatrix
eigenvalues
0
votes
0
answers
22
GATE201612
Consider a $3 \times 3$ matrix with every element being equal to $1$. Its only nonzero eigenvalue is ________.
asked
Jan 30, 2017
in
Linear Algebra
by
makhdoom ghaya
(
9.3k
points)
gate2016ee1
characteristicequation
diagonalizingmatrices
invertiblematrix
numericalanswers
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Recent questions and answers in Linear Algebra
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