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Recent questions and answers in Linear Algebra
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virtual gate
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Linear Algebra
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Prince Sindhiya
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virtualgate
testseries
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2
virtual gate test linear algebra
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Linear Algebra
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Prince Sindhiya
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virtualgate
testseries
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3
number of linearly indendent eigen vectors
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1 day
ago
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Linear Algebra
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MIRIYALA JEEVAN KUMA
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linearalgebra
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+6
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4
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4
GATE19871xxi
If $a, b,$ and $c$ are constants, which of the following is a linear inequality? $ax+bcy=0$ $ax^{2}+cy^{2}=21$ $abx+a^{2}y \geq 15$ $xy+ax \geq 20$
answered
4 days
ago
in
Linear Algebra
by
rohittulasyan
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99
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536
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gate1987
linearalgebra
inequality
+18
votes
3
answers
5
GATE200427
Let $A, B, C, D$ be $n \times n$ matrices, each with nonzero determinant. If $ABCD = I$, then $B^{1}$ is $D^{1}C^{1}A^{1}$ $CDA$ $ADC$ Does not necessarily exist
answered
6 days
ago
in
Linear Algebra
by
Syeda97
(
29
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2.1k
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gate2004
linearalgebra
normal
matrices
+9
votes
3
answers
6
GATE19962.6
The matrices $\begin{bmatrix} \cos\theta && \sin\theta \\ \sin\theta && \cos\theta \end{bmatrix}$ and $\begin{bmatrix} a && 0\\ 0&& b \end{bmatrix}$ commute under multiplication if $a=b \text{ or } \theta = n\pi, n$ an integer always never if $a \cos\theta = b \sin\theta$
answered
6 days
ago
in
Linear Algebra
by
rohittulasyan
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99
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603
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gate1996
linearalgebra
normal
matrices
0
votes
1
answer
7
Work book
answered
Oct 6
in
Linear Algebra
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Mk Utkarsh
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19.5k
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29
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0
votes
0
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8
Test series
asked
Oct 5
in
Linear Algebra
by
abhishekmehta4u
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23.9k
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42
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eigenvalue
+14
votes
4
answers
9
GATE20025a
Obtain the eigen values of the matrix $$A=\begin {bmatrix} 1 & 2 & 34 & 49 \\ 0 & 2 & 43 & 94 \\ 0 & 0 & 2 & 104 \\ 0 & 0 & 0 & 1 \end{bmatrix}$$
answered
Oct 5
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Linear Algebra
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air1ankit
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gate2002
linearalgebra
eigenvalue
normal
descriptive
0
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0
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10
Linear Algebra
We know, the eigen value for upper triangular/lower triangular/diagonal matrices are the diagonal elements of the matrix. https://gateoverflow.in/858/gate20025a This question, https://gateoverflow.in/1174/gate200549 If apply row transformation to convert it ... make the given matrix to upper triangular matrix, so that eigen values will be equal to the elements in the diagonals?
asked
Oct 5
in
Linear Algebra
by
Swapnil Naik
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1.2k
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27
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linearalgebra
engineeringmathematics
eigenvalue
+1
vote
1
answer
11
GATE2016 37 Mathematics
Let $M = \begin{bmatrix} a & b &c \\ b &d & e\\ c & e & f \end{bmatrix}$ be a real matrix with eigenvalues 1, 0 and 3. If the eigenvectors corresponding to 1 and 0 are $\left ( 1,1,1 \right )^T$ and $\left ( 1,1, 0 \right )^T$ respectively, then the value of 3f is equal to _______.
answered
Oct 4
in
Linear Algebra
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MiNiPanda
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14.7k
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85
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linearalgebra
eigenvalue
+1
vote
0
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12
SELF DOUBT
consider a system of linear equation where AMxN XNx1 =BMx1 TRUE OR FALSE Q1 IF B=0 AND DETERMINENT OF A i.e A IS NOT EQUAL TO ZERO THEN IT MEANS UNIQUE SOLUTION?? Q2 IF B NOT EQUAL TO 0 AND DETERMINENT OF A i.e A IS NOT EQUAL TO ZERO THEN IT MEANS INFINITE MANY SOLUTION SOLUTION?? Q3 IF B IS NOT EQUAL TO 0 AND M<N THEN IT MEANS NO UNIQUE SOLUTION??
asked
Oct 3
in
Linear Algebra
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eyeamgj
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5k
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15
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systemofequations
+2
votes
1
answer
13
GATE 2017: Maths: LA
Is manual calculation required to solve this question, or there is some properties can be applied here, btw please solve it.
answered
Oct 2
in
Linear Algebra
by
ami
(
29
points)

288
views
gate_2017
linearalgebra
engineeringmathematics
0
votes
1
answer
14
Linear Algebra RGPV 2001
Test the consistency of the following system of equations and solve if possible $3x + 3y +2z = 1$ $x + 2y = 4$ $10y + 3z = 2$ $2x  3y z = 5$
answered
Sep 30
in
Linear Algebra
by
srestha
Veteran
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98.3k
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39
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linearalgebra
engineeringmathematics
systemofequations
+17
votes
4
answers
15
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
Sep 29
in
Linear Algebra
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Mk Utkarsh
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19.5k
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1.9k
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gate20153
linearalgebra
systemofequations
normal
0
votes
1
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16
Hk Dass Linear Algebra
Test the consistency of the following system of equations $5x + 3y + 7z = 4 $ $3x + 26y + 2z = 9$ $7x + 2y + 10z = 5$
answered
Sep 29
in
Linear Algebra
by
arvin
Loyal
(
9.4k
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24
views
linearalgebra
systemofequations
+3
votes
2
answers
17
Eigen Value
An orthogonal matrix A has eigen values 1, 2 and 4. What is the trace of the matrix
answered
Sep 27
in
Linear Algebra
by
Priyanka Singh 6
(
19
points)

48
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matrices
eigenvalue
+1
vote
3
answers
18
Gate CE 2005 linear algebra
Consider a non homogeneous system of linear equations representing mathematically an over determined system. Such a system will be (A) consistent having a unique solution (B) consistent having many solutions (C) inconsistent having a unique solution (D) inconsistent having no solution
answered
Sep 23
in
Linear Algebra
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Deepakk Poonia (Dee)
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18.7k
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376
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engineeringmathematics
linearalgebra
0
votes
1
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19
Linear system of equations
answered
Sep 16
in
Linear Algebra
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abhishekmehta4u
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23.9k
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21
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engineeringmathematics
linearalgebra
systemofequations
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vote
0
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20
linear algebra
asked
Sep 13
in
Linear Algebra
by
Rohit Kumar 2
(
285
points)

14
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0
votes
0
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21
rank of matrix
how is A will have m1 linearly independent rows and m1 linearly independent columns?
asked
Sep 10
in
Linear Algebra
by
Rohit Kumar 2
(
285
points)

17
views
0
votes
1
answer
22
linear algebra
If the entries in each column of a square matrix M add up to 1, then an Eigen value of M is a) 4 b) 3 c) 2 d) 1 Explain briefly.
answered
Sep 4
in
Linear Algebra
by
ank73811
Junior
(
763
points)

21
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0
votes
1
answer
23
test series ace
please explain all relationship between determinant and determinant of adjoint and so on and also how to derive them in run time during exam if I forget
answered
Aug 31
in
Linear Algebra
by
anuj300998
(
19
points)

18
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0
votes
1
answer
24
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
Aug 23
in
Linear Algebra
by
Mk Utkarsh
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(
19.5k
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32
views
engineeringmathematics
linearalgebra
0
votes
1
answer
25
Chain
Consider F be a family of all subsets of set {1, 2, 3, ..... 100} that contain atleast 50 numbers, partially ordered with respect to containment. Then maximum size of chains in the Poset (F, ⊆) that cover F is ________.  Answer given 51 but why not 100?
answered
Aug 23
in
Linear Algebra
by
ank73811
Junior
(
763
points)

21
views
poset
lattice
0
votes
0
answers
26
Btech
Symmetrical question
asked
Aug 19
in
Linear Algebra
by
S. Sindhu
(
7
points)

11
views
0
votes
1
answer
27
Gate 2015 CE set 2
The two eigen values of the matrix $\begin{bmatrix} 2 & 1\\ 1& p \end{bmatrix}$ have a ratio of 3:1 for p= 2. What is another value of p for which eigenvalues have the same ratio of 3:1? A)2 b) 1 c) 7/3 d)14/3
answered
Aug 18
in
Linear Algebra
by
MiNiPanda
Boss
(
14.7k
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36
views
eigenvalue
usergate2015
usermod
0
votes
0
answers
28
Eigen vector
Is it true that if we have 3 distinct eigen vectors x,y and z than x,y and z would respectively be orthogonal to each other .Please elaborate
asked
Aug 17
in
Linear Algebra
by
Shivangi Parashar 2
(
143
points)

19
views
0
votes
1
answer
29
Gate 2016 CE Set 1
If the entries in each column of a square matrix M add up to 1, then an eigen value of M is A) 4 B) 3 C) 2 D) 1
answered
Aug 17
in
Linear Algebra
by
Shivani gaikawad
Junior
(
523
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52
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eigenvalue
0
votes
0
answers
30
Gate 2016 ME Set 2
The condition for which the eigen values of the matrix A = $\begin{pmatrix} 2 &1 \\ 1& k \end{pmatrix}$ are positive, is a) k>1/2 b) k>2 c) k>0 d) k< 1/2
asked
Aug 17
in
Linear Algebra
by
suparna kar
(
87
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35
views
gate20161
linearalgebra
eigenvalue
+1
vote
1
answer
31
made easy ME previou year question
which on of the following is an eigenvector of the matrix [5 0 0 0 0 5 5 0 0 0 2 1 0 0 3 1] a) [1 2 0 0 ]t b) [0 0 1 0]t c) [1 0 0 2]t d) [1 1 2 1]t
answered
Aug 17
in
Linear Algebra
by
Prince Sindhiya
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(
3.6k
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21
views
matrixeigenvector
0
votes
0
answers
32
Gate2016
A 3×3 matrix p is such that,p^3=p. Then eigen values of p are
asked
Aug 15
in
Linear Algebra
by
lg
(
33
points)

19
views
0
votes
1
answer
33
gate 2014
Two matrices A and B are given below: A= p q r s B= p2 + q2 pr + qs pr +qs r2 + s2 If the rank of matrix A is N, then the rank of matrix B is (A) N /2 (B) N1 (C) N (D) 2 N
answered
Aug 10
in
Linear Algebra
by
arvin
Loyal
(
9.4k
points)

29
views
+1
vote
2
answers
34
Engineering mathematics
if the sum of the diagonal elements of a 2x2 matrix is (6) then the maximum possible value of determinant of the matrix is
answered
Aug 9
in
Linear Algebra
by
Deepanshu
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(
3k
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49
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0
votes
2
answers
35
Engineering Mathematics  Linear Algebra
answered
Aug 9
in
Linear Algebra
by
arvin
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9.4k
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178
views
engineeringmathematics
linearalgebra
0
votes
0
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36
Invertible Matrix
Let $A$ be a nilpotent matrix. Show that $I + A$ is invertible.
asked
Aug 8
in
Linear Algebra
by
pankaj_vir
Loyal
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9.5k
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28
views
engineeringmathematics
linearalgebra
matrices
matrix
0
votes
2
answers
37
Invertible Matrix
Let A be a $5 × 5$ invertible matrix with row sums $1$. That is $\sum_{j=1}^{5} a_{ij} = 1$ for $1 \leq i\leq 5$. Then, what is the sum of all entries of $A^{1}$.
answered
Aug 8
in
Linear Algebra
by
Rishabh Gupta 2
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14.7k
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72
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engineeringmathematics
linearalgebra
matrices
matrix
easy
+3
votes
1
answer
38
TIFR2015MathsA1
Let $A$ be an invertible $10 \times 10$ matrix with real entries such that the sum of each row is $1$. Then The sum of the entries of each row of the inverse of $A$ is $1$. The sum of the entries of each column of the inverse of $A$ is $1$. The trace of the inverse of $A$ is nonzero. None of the above.
answered
Aug 8
in
Linear Algebra
by
Rishabh Gupta 2
Boss
(
14.7k
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128
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tifrmaths2015
linearalgebra
matrices
0
votes
1
answer
39
#idempotent #matrix
If Matrix A and B are of same size and AB=B and BA=A. Then the value of $(A+B)^{5}$ is _____________?
answered
Aug 8
in
Linear Algebra
by
arvin
Loyal
(
9.4k
points)

31
views
+29
votes
4
answers
40
GATE2017131
Let $A$ be $n\times n$ real valued square symmetric matrix of rank 2 with $\sum_{i=1}^{n}\sum_{j=1}^{n}A^{2}_{ij} =$ 50. Consider the following statements. One eigenvalue must be in $\left [ 5,5 \right ]$ The eigenvalue with the largest ... greater than 5 Which of the above statements about eigenvalues of $A$ is/are necessarily CORRECT? Both I and II I only II only Neither I nor II
answered
Jul 20
in
Linear Algebra
by
Gyanu
(
57
points)

3.8k
views
gate20171
linearalgebra
eigenvalue
normal
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