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
First time here? Checkout the
FAQ
!
x
×
Close
Use the google search bar on side panel. It searches through all previous GATE/other questions. For hardcopy of previous year questions please see
here
Recent questions and answers in Linear Algebra
+1
vote
1
answer
1
Gatebook Test
answered
23 hours
ago
in
Linear Algebra
by
aditi19
Active
(
4.9k
points)

43
views
0
votes
1
answer
2
Gatebook Test
answered
23 hours
ago
in
Linear Algebra
by
aditi19
Active
(
4.9k
points)

44
views
+8
votes
5
answers
3
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
in
Linear Algebra
by
sujeetkumar
(
11
points)

1k
views
gate2007it
cartesiancoordinates
+1
vote
3
answers
4
ISI2018MMA12
The rank of the matrix $\begin{bmatrix} 1 &2 &3 &4 \\ 5& 6 & 7 & 8 \\ 6 & 8 & 10 & 12 \\ 151 & 262 & 373 & 484 \end{bmatrix}$ $1$ $2$ $3$ $4$
answered
Sep 23
in
Linear Algebra
by
aditi19
Active
(
4.9k
points)

108
views
isi2018mma
engineeringmathematics
linearalgebra
rankofmatrix
0
votes
2
answers
5
ISI2018MMA13
If $A =\begin{bmatrix} 2 &i \\ i & 0 \end{bmatrix}$ , the trace of $A^{10}$ is $2$ $2(1+i)$ $0$ $2^{10}$
answered
Sep 23
in
Linear Algebra
by
aditi19
Active
(
4.9k
points)

73
views
isi2018mma
engineeringmathematics
linearalgebra
determinant
+24
votes
5
answers
6
GATE2016105
Two eigenvalues of a $3 \times 3$ real matrix $P$ are $(2+\sqrt {1})$ and $3$. The determinant of $P$ is _______
answered
Sep 19
in
Linear Algebra
by
neeraj2681
(
33
points)

3.6k
views
gate20161
linearalgebra
eigenvalue
numericalanswers
normal
0
votes
2
answers
7
GATE2007 EE
Let $x$ and $y$ be two vectors in a $3$ dimensional space and $<x,y>$ denote their dot product. Then the determinant $det\begin{bmatrix}<x,x> & <x,y>\\ <y,x> & <y,y>\end{bmatrix}$ is zero when $x$ and $y$ are linearly ... $x$ and $y$ are linearly independent is nonzero for all nonzero $x$ and $y$ is zero only when either $x$ or $y$ is zero
answered
Sep 11
in
Linear Algebra
by
Pratik Gawali
Active
(
1k
points)

311
views
engineeringmathematics
linearalgebra
+10
votes
3
answers
8
GATE19941.9
The rank of matrix $\begin{bmatrix} 0 & 0 & 3 \\ 9 & 3 & 5 \\ 3 & 1 & 1 \end{bmatrix}$ is: $0$ $1$ $2$ $3$
answered
Sep 7
in
Linear Algebra
by
Prafful
(
13
points)

966
views
gate1994
linearalgebra
matrices
easy
+27
votes
5
answers
9
GATE200623
$F$ is an $n\times n$ real matrix. $b$ is an $n\times 1$ real vector. Suppose there are two $n\times 1$ vectors, $u$ and $v$ such that, $u ≠ v$ and $Fu = b, Fv = b$. Which one of the following statements is false? Determinant of $F$ is zero. There are an infinite number of solutions to $Fx = b$ There is an $x≠0$ such that $Fx = 0$ $F$ must have two identical rows
answered
Aug 27
in
Linear Algebra
by
JashanArora
Junior
(
827
points)

2.2k
views
gate2006
linearalgebra
normal
matrices
+15
votes
5
answers
10
GATE2005IT3
The determinant of the matrix given below is $\begin{bmatrix} 0 &1 &0 &2 \\ 1& 1& 1& 3\\ 0&0 &0 & 1\\ 1& 2& 0& 1 \end{bmatrix}$ $1$ $0$ $1$ $2$
answered
Aug 5
in
Linear Algebra
by
Satbir
Boss
(
19.5k
points)

1.9k
views
gate2005it
linearalgebra
normal
determinant
+10
votes
3
answers
11
GATE20021.1
The rank of the matrix $\begin{bmatrix} 1 & 1 \\ 0 & 0 \end{bmatrix}$ is $4$ $2$ $1$ $0$
answered
Jul 31
in
Linear Algebra
by
thambu
(
11
points)

866
views
gate2002
linearalgebra
easy
matrices
0
votes
1
answer
12
MADE EASY
The Necessary condition to diagonalize a matrix is that A) ITS all eigen values should be distdist B) its eigen vectors should be indeindepent C) its eigen values should be real D) matrix is non singular
answered
Jul 30
in
Linear Algebra
by
Jyotish Ranjan
(
11
points)

58
views
+46
votes
7
answers
13
GATE2014247
The product of the nonzero eigenvalues of the matrix is ____ $\begin{pmatrix} 1 & 0 & 0 & 0 & 1 \\ 0 & 1 & 1 & 1 & 0 \\ 0 & 1 & 1 & 1 & 0 \\ 0 & 1 & 1 & 1 & 0 \\ 1 & 0 & 0 & 0 & 1 \end{pmatrix}$
answered
Jul 24
in
Linear Algebra
by
srestha
Veteran
(
116k
points)

9.6k
views
gate20142
linearalgebra
eigenvalue
normal
numericalanswers
+1
vote
1
answer
14
GATE19989
Derive the expressions for the number of operations required to solve a system of linear equations in $n$ unknowns using the Gaussian Elimination Method. Assume that one operation refers to a multiplication followed by an addition.
answered
Jun 21
in
Linear Algebra
by
suraj
Loyal
(
6k
points)

304
views
gate1998
linearalgebra
systemofequations
descriptive
+37
votes
3
answers
15
GATE200725
Let A be a $4 \times 4$ matrix with eigen values 5,2,1,4. Which of the following is an eigen value of the matrix$\begin{bmatrix} A & I \\ I & A \end{bmatrix}$, where $I$ is the $4 \times 4$ identity matrix? $5$ $7$ $2$ $1$
answered
Jun 15
in
Linear Algebra
by
Ashwani Kumar 2
Boss
(
15.4k
points)

3.1k
views
gate2007
eigenvalue
linearalgebra
difficult
+2
votes
2
answers
16
GATE198816i
Assume that the matrix $A$ given below, has factorization of the form $LU=PA$, where $L$ is lowertriangular with all diagonal elements equal to 1, $U$ is uppertriangular, and $P$ is a permutation matrix. For $A = \begin{bmatrix} 2 & 5 & 9 \\ 4 & 6 & 5 \\ 8 & 2 & 3 \end{bmatrix}$ Compute $L, U,$ and $P$ using Gaussian elimination with partial pivoting.
answered
Jun 8
in
Linear Algebra
by
ankitgupta.1729
Boss
(
15.4k
points)

293
views
gate1988
normal
descriptive
linearalgebra
matrices
0
votes
1
answer
17
Linear Algebra (Self Doubt)
Let $A$ be a $n \times n$ square matrix whose all columns are independent. Is $Ax = b$ always solvable? Actually, I know that $Ax= b$ is solvable if $b$ is in the column space of $A$. However, I am not sure if it is solvable for all values of $b$.
answered
Jun 7
in
Linear Algebra
by
Sourajit25
Active
(
1.2k
points)

96
views
linearalgebra
+17
votes
4
answers
18
GATE200727
Consider the set of (column) vectors defined by$X = \left \{x \in R^3 \mid x_1 + x_2 + x_3 = 0, \text{ where } x^T = \left[x_1,x_2,x_3\right]^T\right \}$ ... a linearly independent set, but it does not span $X$ and therefore is not a basis of $X$. $X$ is not a subspace of $R^3$. None of the above
answered
Jun 6
in
Linear Algebra
by
ankitgupta.1729
Boss
(
15.4k
points)

3.2k
views
gate2007
linearalgebra
normal
vectorspace
0
votes
1
answer
19
GATE 2019:EC
The value of integral $\int_{0}^{\pi }\int_{y}^{\pi }\frac{\sin x}{x}dxdy$ is equal to_________
answered
Jun 3
in
Linear Algebra
by
srestha
Veteran
(
116k
points)

74
views
discretemathematics
+2
votes
4
answers
20
GATE2017 EC
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 ________. Ans 5?
answered
Jun 3
in
Linear Algebra
by
Debargha Bhattacharj
Junior
(
653
points)

198
views
discretemathematics
matrix
+20
votes
3
answers
21
GATE2015118
In the LU decomposition of the matrix $\begin{bmatrix}2 & 2 \\ 4 & 9\end{bmatrix}$, if the diagonal elements of $U$ are both $1$, then the lower diagonal entry $l_{22}$ of $L$ is_________________.
answered
Jun 2
in
Linear Algebra
by
ankitgupta.1729
Boss
(
15.4k
points)

2.8k
views
gate20151
linearalgebra
matrices
numericalanswers
0
votes
2
answers
22
GATE 2017:EC
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 $A$ has only one real eigen value. Then the real eigen value of $A$ is ________
[closed]
answered
Jun 2
in
Linear Algebra
by
Satbir
Boss
(
19.5k
points)

152
views
discretemathematics
linearalgebra
matrix
matrices
+1
vote
1
answer
23
TIFR2014MathsA11
Let $A$ be an $n \times n$ matrix with real entries such that $A^{k}=0$ (0matrix), for some $k \in \mathbb{N}$. Then $A$ has to be the $0$ matrix Trace$(A)$ could be nonzero $A$ is diagonalizable $0$ is the only eigenvalue of $A$.
answered
May 31
in
Linear Algebra
by
Yash4444
Junior
(
609
points)

82
views
tifrmaths2014
linearalgebra
matrices
0
votes
1
answer
24
SelfDoubt: Diagonalizable Matrix
$1)$ How to find a matrix is diagonalizable or not? Suppose a matrix is $A=\begin{bmatrix} \cos \Theta &\sin \Theta \\ \sin\Theta & \cos\Theta \end{bmatrix}$ Is it diagonalizable? $2)$ What is it’s eigen spaces?
answered
May 30
in
Linear Algebra
by
lolster
(
233
points)

136
views
engineeringmathematics
linearalgebra
matrices
+16
votes
3
answers
25
GATE200341
Consider the following system of linear equations ... are linearly dependent. For how many values of $\alpha$, does this system of equations have infinitely many solutions? \(0\) \(1\) \(2\) \(3\)
answered
May 29
in
Linear Algebra
by
MRINMOY_HALDER
Active
(
2.6k
points)

3k
views
gate2003
linearalgebra
systemofequations
normal
0
votes
0
answers
26
GATE MOCK 2018
An orthogonal matrix A has eigen values 1, 2 and 4, then trace of the matrix $A^T$ is ___________
[closed]
asked
May 28
in
Linear Algebra
by
Hirak
Active
(
3.5k
points)

69
views
eigenvalue
linearalgebra
+9
votes
1
answer
27
Mathematics GATE EE
The maximum value of a such that the matrix below has three linearly independent real eigen vectors is $\begin{pmatrix} 3& 0 &2 \\ 1& 1 & 0\\ 0& a & 2 \end{pmatrix}$ (a) $\frac{2}{3\sqrt{3}}$ (b) $\frac{1}{3\sqrt{3}}$ (c) $\frac{1+2\sqrt{3}}{3\sqrt{3}}$ (d)$\frac{1+\sqrt{3}}{3\sqrt{3}}$
answered
May 27
in
Linear Algebra
by
Aishvarya Akshaya Vi
(
39
points)

543
views
engineeringmathematics
gate2015ee
+18
votes
3
answers
28
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
May 27
in
Linear Algebra
by
MRINMOY_HALDER
Active
(
2.6k
points)

2.5k
views
gate2012
linearalgebra
eigenvalue
0
votes
2
answers
29
Engineering Maths
If A = $\begin{bmatrix} 1 & 1 & 0 \\ 0 & 2 &2 \\ 0& 0 & 3 \end{bmatrix}$ then trace of the matrix 3A2 + adj A is ____
answered
May 26
in
Linear Algebra
by
abhishekmehta4u
Boss
(
35.1k
points)

84
views
engineeringmathematics
linearalgebra
+1
vote
1
answer
30
ISI2018PCBA1
Consider a $n \times n$ matrix $A=I_n\alpha\alpha^T$, where $I_n$ is the $n\times n$ identity matrix and $\alpha$ is an $n\times 1$ column vector such that $\alpha^T\alpha=1$.Show that $A^2=A$.
answered
May 20
in
Linear Algebra
by
Kaustubh Vande
(
21
points)

64
views
isi2018pcba
engineeringmathematics
linearalgebra
matrices
descriptive
0
votes
1
answer
31
#GATE 2014 IN
answered
May 14
in
Linear Algebra
by
Satbir
Boss
(
19.5k
points)

31
views
0
votes
1
answer
32
ISI2018MMA14
Let $A$ be a $3× 3$ real matrix with all diagonal entries equal to $0$. If $1 + i$ is an eigenvalue of $A$, the determinant of $A$ equals $4$ $2$ $2$ $4$
answered
May 11
in
Linear Algebra
by
Verma Ashish
Boss
(
10.7k
points)

72
views
isi2018mma
engineeringmathematics
linearalgebra
eigenvalue
determinant
0
votes
2
answers
33
ISI2019MMA13
Let $V$ be the vector space of all $4 \times 4$ matrices such that the sum of the elements in any row or any column is the same. Then the dimension of $V$ is $8$ $10$ $12$ $14$
answered
May 9
in
Linear Algebra
by
pratekag
Active
(
2k
points)

187
views
isi2019mma
engineeringmathematics
linearalgebra
+1
vote
1
answer
34
ISI2019MMA23
Let $A$ be $2 \times 2$ matrix with real entries. Now consider the function $f_A(x)$ = $Ax$ . If the image of every circle under $f_A$ is a circle of the same radius, then A must be an orthogonal matrix A must be a symmetric matrix A must be a skewsymmetric matrix None of the above must necessarily hold
answered
May 7
in
Linear Algebra
by
pratekag
Active
(
2k
points)

125
views
isi2019mma
engineeringmathematics
linearalgebra
0
votes
2
answers
35
ISI2019MMA15
The rank of the matrix $\begin{bmatrix} 0 &1 &t \\ 2& t & 1\\ 2& 2 & 0 \end{bmatrix}$ equals $3$ for any real number $t$ $2$ for any real number $t$ $2$ or $3$ depending on the value of $t$ $1,2$ or $3$ depending on the value of $t$
answered
May 7
in
Linear Algebra
by
Shikha Mallick
Active
(
3.4k
points)

156
views
isi2019mma
linearalgebra
engineeringmathematics
+1
vote
1
answer
36
ISI2019MMA14
If the system of equations $\begin{array} \\ax +y+z= 0 \\ x+by +z = 0 \\ x+y + cz = 0 \end{array}$ with $a,b,c \neq 1$ has a non trivial solutions, the value of $\frac{1}{1a} + \frac{1}{1b} + \frac{1}{1c}$ is $1$ $1$ $3$ $3$
answered
May 7
in
Linear Algebra
by
MRINMOY_HALDER
Active
(
2.6k
points)

143
views
isi2019mma
linearalgebra
systemofequations
+10
votes
4
answers
37
GATE199610
Let $A = \begin{bmatrix} a_{11} && a_{12} \\ a_{21} && a_{22} \end{bmatrix} \text { and } B = \begin{bmatrix} b_{11} && b_{12} \\ b_{21} && b_{22} \end{bmatrix}$ be two matrices such that $AB=I$. Let $C = A \begin{bmatrix} 1 && 0 \\ 1 && 1 \end{bmatrix}$ and $CD =I$. Express the elements of $D$ in terms of the elements of $B$.
answered
May 3
in
Linear Algebra
by
MRINMOY_HALDER
Active
(
2.6k
points)

685
views
gate1996
linearalgebra
matrices
normal
descriptive
+1
vote
0
answers
38
CSIR UGC NET
asked
Apr 28
in
Linear Algebra
by
Hirak
Active
(
3.5k
points)

49
views
linearalgebra
eigenvalue
matrices
+1
vote
0
answers
39
Made Easy Engineering Maths book
The ans given is b, but i am not able to understande why. According to me the largest eigen value is 2, and therefore none of the option matches..!
asked
Apr 27
in
Linear Algebra
by
Hirak
Active
(
3.5k
points)

81
views
+1
vote
2
answers
40
Virtual Gate Test Series: Linear Algebra  Rank Of The Matrix
answered
Apr 27
in
Linear Algebra
by
SuvasishDutta
Active
(
1.3k
points)

65
views
engineeringmathematics
linearalgebra
matrix
rankofmatrix
virtualgatetestseries
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
Standard Book Exercise Questions for Computer Science
Resource to Learn Graph Theory Interactively
Recruitment to the post of Scientist/Engineer 'SC' (Electronics, Mechanical and Computer Science)
Standard Videos for Calculus
Standard Videos for Linear Algebra
All categories
General Aptitude
1.8k
Engineering Mathematics
7.3k
Discrete Mathematics
5.1k
Probability
987
Linear Algebra
682
Calculus
493
Digital Logic
2.9k
Programming and DS
4.9k
Algorithms
4.4k
Theory of Computation
6.2k
Compiler Design
2.1k
Operating System
4.2k
Databases
4.1k
CO and Architecture
3.4k
Computer Networks
4.1k
Non GATE
1.6k
Others
1.8k
Admissions
595
Exam Queries
576
Tier 1 Placement Questions
23
Job Queries
72
Projects
17
Follow @csegate
Recent questions and answers in Linear Algebra
Recent Blog Comments
Are the answers also present ?
@Arjun sir , Is there any page or something where...
@arjun sir but u called about providing the pdfs...
But anyhow I appreciate this. The questions of...
All these PYQ blogs and standard videos blogs...
50,407
questions
55,863
answers
192,661
comments
91,660
users