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Recent questions in Linear Algebra
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Matrices, determinants,
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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 $b$.
asked
Jun 6
in
Linear Algebra
by
Debargha Bhattacharj
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349
points)

55
views
linearalgebra
0
votes
1
answer
2
GATE 2019:EC
The value of integral $\int_{0}^{\pi }\int_{y}^{\pi }\frac{\sin x}{x}dxdy$ is equal to_________
asked
Jun 2
in
Linear Algebra
by
srestha
Veteran
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111k
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54
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discretemathematics
0
votes
2
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3
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]
asked
Jun 2
in
Linear Algebra
by
srestha
Veteran
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111k
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58
views
discretemathematics
linearalgebra
matrix
matrices
+1
vote
4
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4
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?
asked
Jun 1
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Linear Algebra
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srestha
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111k
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88
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discretemathematics
matrix
0
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0
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5
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
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(
3k
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48
views
eigenvalue
linearalgebra
0
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1
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6
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?
asked
May 27
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Linear Algebra
by
srestha
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111k
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106
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engineeringmathematics
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matrices
0
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1
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7
#GATE 2014 IN
asked
May 12
in
Linear Algebra
by
Aishvarya Akshaya Vi
(
39
points)

28
views
+1
vote
1
answer
8
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 $A^2=A$.
asked
May 12
in
Linear Algebra
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akash.dinkar12
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40.4k
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54
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isi2018pcba
engineeringmathematics
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descriptive
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1
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9
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 $4$ $2$ $2$ $4$
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May 11
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Linear Algebra
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akash.dinkar12
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40.4k
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53
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isi2018
engineeringmathematics
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eigenvalue
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0
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1
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10
ISI2018MMA13
If $A =\begin{bmatrix} 2 &i \\ i & 0 \end{bmatrix}$ , the trace of $A^{10}$ is $2$ $2(1+i)$ $0$ $2^{10}$
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May 11
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Linear Algebra
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akash.dinkar12
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40.4k
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42
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isi2018
engineeringmathematics
linearalgebra
determinant
0
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2
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11
ISI2018MMA12
The rank of the matrix $\begin{bmatrix} 1 &2 &3 &4 \\ 5& 6 & 7 & 8 \\ 6 & 8 & 10 & 12 \\ 151 & 262 & 373 & 484 \end{bmatrix}$ $1$ $2$ $3$ $4$
asked
May 11
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Linear Algebra
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akash.dinkar12
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40.4k
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65
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isi2018
engineeringmathematics
linearalgebra
rankofmatrix
0
votes
1
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12
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
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May 7
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Linear Algebra
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Sayan Bose
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113
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isi2019
engineeringmathematics
linearalgebra
0
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2
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13
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 $t$
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May 7
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Linear Algebra
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Sayan Bose
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145
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isi2019
linearalgebra
engineeringmathematics
0
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1
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14
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 $1$ $1$ $3$ $3$
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May 7
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Linear Algebra
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Sayan Bose
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6.9k
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113
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isi2019
linearalgebra
systemofequations
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2
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15
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 $8$ $10$ $12$ $14$
asked
May 6
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Linear Algebra
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Sayan Bose
Loyal
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173
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isi2019
engineeringmathematics
linearalgebra
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16
CSIR UGC NET
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Apr 28
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Hirak
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36
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liner
linearalgebra
eigenvalue
matrixinversion
matrices
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17
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
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Hirak
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50
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+3
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1
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18
Vani Institute Question Bank Pg231 chapter 6
The Eigen values of $A=\begin{bmatrix} a& 1& 0\\1 &a &1 \\0 &1 &a \end{bmatrix}$ are______ $a,a,a$ $0,a,2a$ $a,2a,2a$ $a,a+\sqrt{2},a\sqrt{2}$
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Apr 25
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Linear Algebra
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Hirak
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85
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engineeringmathematics
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19
ISIMMA201544
Let $P_{1},P_{2},$ and $P_{3}$ denote, respectively, the planes defined by $a_{1}x + b_{1}y + c_{1}z = \alpha _{1}$ $a_{2}x + b_{2}y + c_{2}z = \alpha _{2}$ $a_{3}x + b_{3}y + c_{3}z = \alpha _{3}$ It is given ... then the planes (A) do not have any common point of intersection (B) intersect at a unique point (C) intersect along a straight line (D) intersect along a plane
asked
Feb 22
in
Linear Algebra
by
ankitgupta.1729
Boss
(
13.2k
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81
views
engineeringmathematics
linearalgebra
userisi2015
usermod
+3
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4
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20
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
asked
Feb 7
in
Linear Algebra
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Arjun
Veteran
(
406k
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1.7k
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gate2019
engineeringmathematics
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determinant
+3
votes
3
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21
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 _______
asked
Feb 7
in
Linear Algebra
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Arjun
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406k
points)

2.3k
views
gate2019
numericalanswers
engineeringmathematics
linearalgebra
eigenvalue
0
votes
0
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22
Previous gate
asked
Jan 31
in
Linear Algebra
by
Hemanth_13
Loyal
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6.5k
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76
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eigenvalue
0
votes
0
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23
#math
asked
Jan 30
in
Linear Algebra
by
amit166
(
459
points)

30
views
engineeringmathematics
0
votes
0
answers
24
ace test series
how? please explain
asked
Jan 28
in
Linear Algebra
by
Vignaneswarkrishna
(
167
points)

45
views
0
votes
0
answers
25
Gate 2016 ee
Question number 249
asked
Jan 27
in
Linear Algebra
by
Vignaneswarkrishna
(
167
points)

42
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+1
vote
1
answer
26
Nullity of matrix
Nullity of a matrix = Total number columns – Rank of that matrix By how to calculate value of x when nullity is already given(1 in this case)
asked
Jan 24
in
Linear Algebra
by
Nandkishor3939
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132
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engineeringmathematics
linearalgebra
matrices
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27
acetest series
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Jan 21
in
Linear Algebra
by
Rajesh Panwar
Junior
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673
points)

57
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0
votes
1
answer
28
Simple Determinant
how to prove determinant 1 and 2 are same by some rowcolumn manipulation ,please Help??
asked
Jan 19
in
Linear Algebra
by
BHASHKAR
(
25
points)

57
views
linearalgebra
engineeringmathematics
matrices
0
votes
1
answer
29
Made Easy Workbook
Let A be a 3*3 matrix whose characteristics roots are 3,2,1. If $B=A^2A$ then B=? a)24 b)2 c)12 d)12 Please explain in detail.
asked
Jan 19
in
Linear Algebra
by
Reshu $ingh
(
253
points)

106
views
linearalgebra
matrix
eigenvalue
0
votes
1
answer
30
Ace Test Series 2019: Discrete Maths  Recurrence Relation
asked
Jan 17
in
Linear Algebra
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Rajesh Panwar
Junior
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673
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81
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acetestseries
discretemathematics
recurrenceeqation
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