The Gateway to Computer Science Excellence
For all GATE CSE Questions
Toggle navigation
Facebook Login
or
Email or Username
Password
Remember
Login
Register

I forgot my password
Activity
Questions
Unanswered
Tags
Subjects
Users
Ask
Prev
Blogs
New Blog
Exams
Recent questions and answers in Linear Algebra
+2
votes
2
answers
1
matrix groups
Which of the following is true? Every lower triangular matrix is group under multiplication operation where all elements of diagonal are non zero numbers. Every diagonal matrix is group under multiplication operation, where all elements of diagonal are non zero numbers. Every ... addition operation where all elements are real numbers. Both (a) and b) isn't a b c all are correct?
answered
Jan 4
in
Linear Algebra
by
Sahin
(
361
points)

385
views
grouptheory
+16
votes
3
answers
2
Mathematics: GATE 2013 ECA27
Let A be an mxn matrix and B an nxm matrix. It is given that determinant ( Im + AB ) = determinant ( In + BA ) , where Ik is the k k identity matrix. Using the above property, the determinant of the matrix given below is ... A) 2 B) 5 C) 8 D) 16
answered
Jan 4
in
Linear Algebra
by
Satbir
Boss
(
23.8k
points)

1.3k
views
gate2013ec
linearalgebra
engineeringmathematics
normal
determinant
+7
votes
4
answers
3
GATE201944
Consider the following matrix: $R = \begin{bmatrix} 1 & 2 & 4 & 8 \\ 1 & 3 & 9 & 27 \\ 1 & 4 & 16 & 64 \\ 1 & 5 & 25 & 125 \end{bmatrix}$ The absolute value of the product of Eigen values of $R$ is _______
answered
Jan 2
in
Linear Algebra
by
ankitgupta.1729
Boss
(
17k
points)

3.4k
views
gate2019
numericalanswers
engineeringmathematics
linearalgebra
eigenvalue
+17
votes
5
answers
4
GATE200426
The number of different $n \times n $ symmetric matrices with each element being either 0 or 1 is: (Note: $\text{power} \left(2, X\right)$ is same as $2^X$) $\text{power} \left(2, n\right)$ $\text{power} \left(2, n^2\right)$ $\text{power} \left(2,\frac{ \left(n^2+ n \right) }{2}\right)$ $\text{power} \left(2, \frac{\left(n^2  n\right)}{2}\right)$
answered
Jan 1
in
Linear Algebra
by
JashanArora
Loyal
(
6.2k
points)

3.8k
views
gate2004
linearalgebra
normal
matrices
0
votes
1
answer
5
ISI2017DCG25
If $f(x) = \begin{vmatrix} 2 \cos ^2 x & \sin 2x & – \sin x \\ \sin 2x & 2 \sin ^2 x & \cos x \\ \sin x & – \cos x & 0 \end{vmatrix},$ then $\int_0^{\frac{\pi}{2}} [ f(x) + f’(x)] dx$ is $\pi$ $\frac{\pi}{2}$ $0$ $1$
answered
Dec 30, 2019
in
Linear Algebra
by
ajaysoni1924
Boss
(
10.8k
points)

35
views
isi2017dcg
linearalgebra
determinant
definiteintegrals
nongate
+1
vote
1
answer
6
ISI2015MMA37
Let $a$ be a nonzero real number. Define $f(x) = \begin{vmatrix} x & a & a & a \\ a & x & a & a \\ a & a & x & a \\ a & a & a & x \end{vmatrix}$ for $x \in \mathbb{R}$. Then, the number of distinct real roots of $f(x) =0$ is $1$ $2$ $3$ $4$
answered
Dec 30, 2019
in
Linear Algebra
by
ajaysoni1924
Boss
(
10.8k
points)

53
views
isi2015mma
linearalgebra
determinant
functions
+34
votes
5
answers
7
GATE201713
Let $c_{1}.....c_{n}$ be scalars, not all zero, such that $\sum_{i=1}^{n}c_{i}a_{i}$ = 0 where $a_{i}$ are column vectors in $R^{n}$. Consider the set of linear equations $Ax = b$ ... of equations has a unique solution at $x=J_{n}$ where $J_{n}$ denotes a $n$dimensional vector of all 1. no solution infinitely many solutions finitely many solutions
answered
Dec 25, 2019
in
Linear Algebra
by
mehul vaidya
Loyal
(
5.3k
points)

6.3k
views
gate20171
linearalgebra
systemofequations
normal
+1
vote
1
answer
8
ISI2014DCG38
Suppose that $A$ is a $3 \times 3$ real matrix such that for each $u=(u_1, u_2, u_3)’ \in \mathbb{R}^3, \: u’Au=0$ where $u’$ stands for the transpose of $u$. Then which one of the following is true? $A’=A$ $A’=A$ $AA’=I$ None of these
answered
Dec 16, 2019
in
Linear Algebra
by
aiyyar.aarushi
(
413
points)

59
views
isi2014dcg
linearalgebra
matrices
0
votes
1
answer
9
characteristics polynomial
A is 5×5 matrix, all of whose entries are 1, then (a) A is not diagonalizable (b) A is idempotent (c) A is nilpotent (d) The minimal polynomial and the characteristics polynomial of A are not equal
answered
Dec 13, 2019
in
Linear Algebra
by
facil
(
11
points)

80
views
+5
votes
4
answers
10
ISRO200834
If a square matrix A satisfies $A^TA=I$, then the matrix $A$ is Idempotent Symmetric Orthogonal Hermitian
answered
Dec 3, 2019
in
Linear Algebra
by
JashanArora
Loyal
(
6.2k
points)

1.5k
views
isro2008
linearalgebra
matrices
+6
votes
5
answers
11
GATE20199
Let $X$ be a square matrix. Consider the following two statements on $X$. $X$ is invertible Determinant of $X$ is nonzero Which one of the following is TRUE? I implies II; II does not imply I II implies I; I does not imply II I does not imply II; II does not imply I I and II are equivalent statements
answered
Nov 30, 2019
in
Linear Algebra
by
JashanArora
Loyal
(
6.2k
points)

2.3k
views
gate2019
engineeringmathematics
linearalgebra
determinant
+7
votes
2
answers
12
GATE19952.13
A unit vector perpendicular to both the vectors $a=2i3j+k$ and $b=i+j2k$ is: $\frac{1}{\sqrt{3}} (i+j+k)$ $\frac{1}{3} (i+jk)$ $\frac{1}{3} (ijk)$ $\frac{1}{\sqrt{3}} (i+jk)$
answered
Nov 28, 2019
in
Linear Algebra
by
Satbir
Boss
(
23.8k
points)

1.1k
views
gate1995
linearalgebra
normal
vectorspace
0
votes
1
answer
13
ISI2015MMA44
Let $P_1$, $P_2$ and $P_3$ denote, respectively, the planes defined by $\begin{array} {} a_1x +b_1y+c_1z=\alpha _1 \\ a_2x +b_2y+c_2z=\alpha _2 \\ a_3x +b_3y+c_3z=\alpha _3 \end{array}$ It is given that $P_1$, $P_2$ and $P_3$ ... then the planes do not have any common point of intersection intersect at a unique point intersect along a straight line intersect along a plane
answered
Nov 25, 2019
in
Linear Algebra
by
Lakshman Patel RJIT
Veteran
(
58.7k
points)

27
views
isi2015mma
linearalgebra
systemofequations
+2
votes
2
answers
14
ISI2015MMA39
The eigenvalues of the matrix $X = \begin{pmatrix} 2 & 1 & 1 \\ 1 & 2 & 1 \\ 1 & 1 & 2 \end{pmatrix}$ are $1,1,4$ $1,4,4$ $0,1,4$ $0,4,4$
answered
Nov 25, 2019
in
Linear Algebra
by
Lakshman Patel RJIT
Veteran
(
58.7k
points)

74
views
isi2015mma
linearalgebra
matrices
eigenvalue
0
votes
1
answer
15
ISI2014DCG64
The value of $\lambda$ such that the system of equation $\begin{array}{} 2x & – & y & + & 2z & = & 2 \\ x & – & 2y & + & z & = & 4 \\ x & + & y & + & \lambda z & = & 4 \end{array}$ has no solution is $3$ $1$ $0$ $3$
answered
Nov 24, 2019
in
Linear Algebra
by
Lakshman Patel RJIT
Veteran
(
58.7k
points)

59
views
isi2014dcg
linearalgebra
matrices
systemofequations
+1
vote
1
answer
16
ISI2016DCG31
Let $A$ be an $n\times n$ matrix such that $\mid\: A^{2}\mid=1.\:\: \mid A\:\mid$ stands for determinant of matrix $A.$ Then $\mid\:(A)\mid=1$ $\mid\:(A)\mid=0\:\text{or}\:1$ $\mid\:(A)\mid=1,0\:\text{or}\:1$ $\mid\:(A)\mid=1\:\text{or}\:1$
answered
Nov 18, 2019
in
Linear Algebra
by
Lakshman Patel RJIT
Veteran
(
58.7k
points)

22
views
isi2016dcg
linearalgebra
matrices
determinant
+4
votes
3
answers
17
ISRO200709
Eigen vectors of $\begin{bmatrix} 1 && \cos \theta \\ \cos \theta && 1 \end{bmatrix}$ are $\begin{bmatrix} a^n && 1 \\ 0 && a^n \end{bmatrix}$ $\begin{bmatrix} a^n && n \\ 0 && a^n \end{bmatrix}$ ... $\begin{bmatrix} a^n && na^{n1} \\ n && a^n \end{bmatrix}$
answered
Nov 16, 2019
in
Linear Algebra
by
Viplove04
(
39
points)

2.5k
views
isro2007
linearalgebra
matrices
eigenvalue
+4
votes
5
answers
18
Eigen Value
An orthogonal matrix A has eigen values 1, 2 and 4. What is the trace of the matrix
answered
Nov 12, 2019
in
Linear Algebra
by
JashanArora
Loyal
(
6.2k
points)

330
views
matrices
eigenvalue
+1
vote
3
answers
19
ISI2014DCG8
If $M$ is a $3 \times 3$ matrix such that $\begin{bmatrix} 0 & 1 & 2 \end{bmatrix}M=\begin{bmatrix}1 & 0 & 0 \end{bmatrix}$ and $\begin{bmatrix}3 & 4 & 5 \end{bmatrix} M = \begin{bmatrix}0 & 1 & 0 \end{bmatrix}$ ... $\begin{bmatrix} 1 & 2 & 0 \end{bmatrix}$ $\begin{bmatrix} 9 & 10 & 8 \end{bmatrix}$
answered
Nov 11, 2019
in
Linear Algebra
by
techbd123
Active
(
3.5k
points)

113
views
isi2014dcg
linearalgebra
matrices
+4
votes
2
answers
20
TIFR2018A14
Let $A$ be an $n\times n$ invertible matrix with real entries whose row sums are all equal to $c$. Consider the following statements: Every row in the matrix $2A$ sums to $2c$. Every row in the matrix $A^{2}$ sums to $c^{2}$. Every row in the matrix $A^{1}$ ... $(1)$ and $(2)$ are correct but not necessarily statement $(3)$ all the three statements $(1), (2),$ and $(3)$ are correct
answered
Nov 9, 2019
in
Linear Algebra
by
rohith1001
Active
(
1.9k
points)

555
views
tifr2018
matrices
linearalgebra
+15
votes
2
answers
21
TIFR2013B3
How many $4 \times 4$ matrices with entries from ${0, 1}$ have odd determinant? Hint: Use modulo $2$ arithmetic. $20160$ $32767$ $49152$ $57343$ $65520$
answered
Nov 9, 2019
in
Linear Algebra
by
rohith1001
Active
(
1.9k
points)

1.2k
views
tifr2013
linearalgebra
matrices
+20
votes
4
answers
22
GATE201211
Let A be the $ 2 × 2 $ matrix with elements $a_{11} = a_{12} = a_{21} = +1 $ and $ a_{22} = −1 $ . Then the eigenvalues of the matrix $A^{19}$ are $1024$ and $−1024$ $1024\sqrt{2}$ and $−1024 \sqrt{2}$ $4 \sqrt{2}$ and $−4 \sqrt{2}$ $512 \sqrt{2}$ and $−512 \sqrt{2}$
answered
Oct 31, 2019
in
Linear Algebra
by
Praveenk99
(
83
points)

2.9k
views
gate2012
linearalgebra
eigenvalue
+21
votes
5
answers
23
GATE2015333
If the following system has nontrivial solution, $px + qy + rz = 0$ $qx + ry + pz = 0$ $rx + py + qz = 0$, then which one of the following options is TRUE? $p  q + r = 0 \text{ or } p = q = r$ $p + q  r = 0 \text{ or } p = q = r$ $p + q + r = 0 \text{ or } p = q = r$ $p  q + r = 0 \text{ or } p = q = r$
answered
Oct 30, 2019
in
Linear Algebra
by
techbd123
Active
(
3.5k
points)

3.2k
views
gate20153
linearalgebra
systemofequations
normal
+27
votes
6
answers
24
GATE2017252
If the characteristic polynomial of a 3 $\times$ 3 matrix $M$ over $\mathbb{R}$ (the set of real numbers) is $\lambda^3 – 4 \lambda^2 + a \lambda +30, \quad a \in \mathbb{R}$, and one eigenvalue of $M$ is 2, then the largest among the absolute values of the eigenvalues of $M$ is _______
answered
Oct 28, 2019
in
Linear Algebra
by
techbd123
Active
(
3.5k
points)

4.1k
views
gate20172
engineeringmathematics
linearalgebra
numericalanswers
eigenvalue
+19
votes
2
answers
25
GATE19974.2
Let $A=(a_{ij})$ be an $n$rowed square matrix and $I_{12}$ be the matrix obtained by interchanging the first and second rows of the $n$rowed Identify matrix. Then $AI_{12}$ is such that its first Row is the same as its second row Row is the same as the second row of $A$ Column is the same as the second column of $A$ Row is all zero
answered
Oct 24, 2019
in
Linear Algebra
by
Satbir
Boss
(
23.8k
points)

1.1k
views
gate1997
linearalgebra
easy
matrices
+24
votes
2
answers
26
GATE2017222
Let $P = \begin{bmatrix}1 & 1 & 1 \\2 & 3 & 4 \\3 & 2 & 3\end{bmatrix}$ and $Q = \begin{bmatrix}1 & 2 &1 \\6 & 12 & 6 \\5 & 10 & 5\end{bmatrix}$ be two matrices. Then the rank of $ P+Q$ is ___________ .
answered
Oct 24, 2019
in
Linear Algebra
by
Satbir
Boss
(
23.8k
points)

3.1k
views
gate20172
linearalgebra
eigenvalue
numericalanswers
+9
votes
3
answers
27
GATE200549
What are the eigenvalues of the following $2\times 2$ matrix? $\left( \begin{array}{cc} 2 & 1\\ 4 & 5\end{array}\right)$ $1$ and $1$ $1$ and $6$ $2$ and $5$ $4$ and $1$
answered
Oct 23, 2019
in
Linear Algebra
by
Satbir
Boss
(
23.8k
points)

962
views
gate2005
linearalgebra
eigenvalue
easy
+1
vote
1
answer
28
Gatebook Test
answered
Oct 22, 2019
in
Linear Algebra
by
aditi19
Active
(
5.2k
points)

55
views
0
votes
1
answer
29
Gatebook Test
answered
Oct 22, 2019
in
Linear Algebra
by
aditi19
Active
(
5.2k
points)

54
views
+1
vote
1
answer
30
ISI2015MMA61
Let $ A = \begin{pmatrix} 1 & 1 & 1 \\ 1 & 2 & 2 \\ 1 & 2 & 3 \end{pmatrix} \text{ and } B=\begin{pmatrix} 1 & 0 & 0 \\ 1 & 1 & 0 \\ 1 & 1 & 1 \end{pmatrix}.$ Then there exists a matrix $C$ ... no matrix $C$ such that $A=BC$ there exists a matrix $C$ such that $A=BC$, but $A \neq CB$ there is no matrix $C$ such that $A=CB$
answered
Oct 19, 2019
in
Linear Algebra
by
chirudeepnamini
Active
(
4.3k
points)

37
views
isi2015mma
linearalgebra
matrices
0
votes
1
answer
31
ISI2015MMA43
The values of $\eta$ for which the following system of equations $\begin{array} {} x & + & y & + & z & = & 1 \\ x & + & 2y & + & 4z & = & \eta \\ x & + & 4y & + & 10z & = & \eta ^2 \end{array}$ has a solution are $\eta = 1, 2$ $\eta = 1, 2$ $\eta = 3, 3$ $\eta = 1, 2$
answered
Oct 19, 2019
in
Linear Algebra
by
chirudeepnamini
Active
(
4.3k
points)

27
views
isi2015mma
linearalgebra
systemofequations
+9
votes
5
answers
32
GATE2007IT80
Let $P_{1},P_{2},\ldots,P_{n}$ be $n$ points in the $xy$plane such that no three of them are collinear. For every pair of points $P_{i}$ and $P_{j}$, let $L_{ij}$ be the line passing through them. Let $L_{ab}$ be the line with the ... largest or the smallest $y$coordinate among all the points The difference between $x$coordinates $P_{a}$ and $P_{b}$ is minimum None of the above
answered
Oct 4, 2019
in
Linear Algebra
by
sujeetkumar
(
15
points)

1.2k
views
gate2007it
cartesiancoordinates
+1
vote
1
answer
33
ISI2014DCG9
The values of $\eta$ for which the following system of equations $\begin{array} {} x & + & y & + & z & = & 1 \\ x & + & 2y & + & 4z & = & \eta \\ x & + & 4y & + & 10z & = & \eta ^2 \end{array}$ has a solution are $\eta=1, 2$ $\eta=1, 2$ $\eta=3, 3$ $\eta=1, 2$
answered
Sep 29, 2019
in
Linear Algebra
by
techbd123
Active
(
3.5k
points)

74
views
isi2014dcg
linearalgebra
systemofequations
0
votes
1
answer
34
ISI2015MMA63
Let $\theta=2\pi/67$. Now consider the matrix $A = \begin{pmatrix} \cos \theta & \sin \theta \\  \sin \theta & \cos \theta \end{pmatrix}$. Then the matrix $A^{2010}$ ... $\begin{pmatrix} 0 & 1 \\ 1 & 0 \end{pmatrix}$
answered
Sep 25, 2019
in
Linear Algebra
by
`JEET
Boss
(
18.9k
points)

23
views
isi2015mma
linearalgebra
matrices
0
votes
1
answer
35
ISI2015MMA62
If the matrix $A = \begin{bmatrix} a & 1 \\ 2 & 3 \end{bmatrix}$ has $1$ as an eigenvalue, then $\textit{trace}(A)$ is $4$ $5$ $6$ $7$
answered
Sep 25, 2019
in
Linear Algebra
by
Verma Ashish
Boss
(
12.9k
points)

47
views
isi2015mma
linearalgebra
matrices
eigenvalue
+1
vote
1
answer
36
ISI2014DCG25
The determinant $\begin{vmatrix} b+c & c+a & a+b \\ q+r & r+p & p+q \\ y+z & z+x & x+y \end{vmatrix}$ equals $\begin{vmatrix} a & b & c \\ p & q & r \\ x & y & z \end{vmatrix}$ ... $3\begin{vmatrix} a & b & c \\ p & q & r \\ x & y & z \end{vmatrix}$ None of these
answered
Sep 24, 2019
in
Linear Algebra
by
`JEET
Boss
(
18.9k
points)

60
views
isi2014dcg
linearalgebra
determinant
0
votes
0
answers
37
ISI2014DCG70
For the matrices $A = \begin{pmatrix} a & a \\ 0 & a \end{pmatrix}$ and $B = \begin{pmatrix} 0 & 1 \\ 1 & 0 \end{pmatrix}$, $(B^{1}AB)^3$ is equal to $\begin{pmatrix} a^3 & a^3 \\ 0 & a^3 \end{pmatrix}$ ... $\begin{pmatrix} a^3 & 0 \\ 3a^3 & a^3 \end{pmatrix}$ $\begin{pmatrix} a^3 & 0 \\ 3a^3 & a^3 \end{pmatrix}$
asked
Sep 23, 2019
in
Linear Algebra
by
Arjun
Veteran
(
430k
points)

35
views
isi2014dcg
linearalgebra
matrices
inverse
0
votes
0
answers
38
ISI2015MMA38
A real $2 \times 2$ matrix $M$ such that $M^2 = \begin{pmatrix} 1 & 0 \\ 0 & 1 \varepsilon \end{pmatrix}$ exists for all $\varepsilon > 0$ does not exist for any $\varepsilon > 0$ exists for some $\varepsilon > 0$ none of the above is true
asked
Sep 23, 2019
in
Linear Algebra
by
Arjun
Veteran
(
430k
points)

25
views
isi2015mma
linearalgebra
matrices
0
votes
0
answers
39
ISI2015MMA40
Let $x_1, x_2, x_3, x_4, y_1, y_2, y_3$ and $y_4$ be fixed real numbers, not all of them equal to zero. Define a $4 \times 4$ matrix $\textbf{A}$ ... $(\textbf{A})$ equals $1$ or $2$ $0$ $4$ $2$ or $3$
asked
Sep 23, 2019
in
Linear Algebra
by
Arjun
Veteran
(
430k
points)

35
views
isi2015mma
linearalgebra
matrices
rankofmatrix
0
votes
0
answers
40
ISI2015MMA42
Let $\lambda_1, \lambda_2, \lambda_3$ denote the eigenvalues of the matrix $A \begin{pmatrix} 1 & 0 & 0 \\ 0 & \cos t & \sin t \\ 0 &  \sin t & \cos t \end{pmatrix}.$ If $\lambda_1+\lambda_2+\lambda_3 = \sqrt{2}+1$ ... $\{  \frac{\pi}{4}, \frac{\pi}{4} \}$ $\{  \frac{\pi}{3}, \frac{\pi}{3} \}$
asked
Sep 23, 2019
in
Linear Algebra
by
Arjun
Veteran
(
430k
points)

39
views
isi2015mma
linearalgebra
matrices
eigenvalue
To see more, click for all the
questions in this category
.
Quick search syntax
tags
tag:apple
author
user:martin
title
title:apple
content
content:apple
exclude
tag:apple
force match
+apple
views
views:100
score
score:10
answers
answers:2
is accepted
isaccepted:true
is closed
isclosed:true
Recent Posts
ISRO CSE 2020 PAPER ANALYSE
BARC OCES/DGFS 2020
ISI CMI PDF by GATE Overflow
Management Trainee Recruitment COAL INDIA 2020
ECIL Interview Experience
All categories
General Aptitude
1.9k
Engineering Mathematics
7.5k
Discrete Mathematics
5.2k
Probability
1k
Linear Algebra
723
Calculus
592
Digital Logic
2.9k
Programming and DS
4.9k
Algorithms
4.4k
Theory of Computation
6.2k
Compiler Design
2.1k
Operating System
4.5k
Databases
4.1k
CO and Architecture
3.4k
Computer Networks
4.2k
Non GATE
1.4k
Others
1.4k
Admissions
595
Exam Queries
573
Tier 1 Placement Questions
23
Job Queries
72
Projects
18
Follow @csegate
Recent questions and answers in Linear Algebra
Recent Blog Comments
they were in hurry while setting the papers they...
@Swaraj Right.. In Little Endian  Big endian...
Q42 C option is correct for C set as it is an...
@ smsubham The SQL query question No...
Are SQL query and that case 1, case 2 answer in...
50,737
questions
57,271
answers
198,140
comments
104,781
users