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Recent questions tagged linearalgebra
Webpage for Linear Algebra
0
votes
1
answer
1
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
Junior
(
643
points)

92
views
linearalgebra
0
votes
2
answers
2
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 ________
asked
Jun 2
in
Linear Algebra
by
srestha
Veteran
(
116k
points)

147
views
discretemathematics
linearalgebra
matrix
matrices
0
votes
0
answers
3
GATE MOCK 2018
An orthogonal matrix A has eigen values 1, 2 and 4, then trace of the matrix $A^T$ is ___________
asked
May 28
in
Linear Algebra
by
Hirak
Active
(
3.4k
points)

69
views
eigenvalue
linearalgebra
0
votes
1
answer
4
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
in
Linear Algebra
by
srestha
Veteran
(
116k
points)

135
views
engineeringmathematics
linearalgebra
matrices
0
votes
0
answers
5
Self DoubtLA
In a nonhomogeneous equation Ax = b, x has a unique solution when $A^{1}$ exists i.e x = $A^{1}$b but when det(A) = 0 then we have infinite solution or many solution. please give a mathematical explanation of how the 2nd statement occurs?
asked
May 26
in
Mathematical Logic
by
MRINMOY_HALDER
Active
(
2.5k
points)

36
views
linearalgebra
systemofequations
+4
votes
0
answers
6
IISc CSA  Research Interview Question
Prove that the rank of the Adjacency Matrix which is associated with a $k$ regular graph is $k.$
asked
May 22
in
Graph Theory
by
ankitgupta.1729
Boss
(
15.3k
points)

86
views
graphtheory
linearalgebra
+1
vote
1
answer
7
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
by
akash.dinkar12
Boss
(
41.6k
points)

63
views
isi2018pcba
engineeringmathematics
linearalgebra
matrices
descriptive
0
votes
1
answer
8
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 $4$ $2$ $2$ $4$
asked
May 11
in
Linear Algebra
by
akash.dinkar12
Boss
(
41.6k
points)

69
views
isi2018mma
engineeringmathematics
linearalgebra
eigenvalue
determinant
0
votes
2
answers
9
ISI2018MMA13
If $A =\begin{bmatrix} 2 &i \\ i & 0 \end{bmatrix}$ , the trace of $A^{10}$ is $2$ $2(1+i)$ $0$ $2^{10}$
asked
May 11
in
Linear Algebra
by
akash.dinkar12
Boss
(
41.6k
points)

71
views
isi2018mma
engineeringmathematics
linearalgebra
determinant
+1
vote
3
answers
10
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
in
Linear Algebra
by
akash.dinkar12
Boss
(
41.6k
points)

106
views
isi2018mma
engineeringmathematics
linearalgebra
rankofmatrix
0
votes
1
answer
11
ISI2018MMA11
The value of $\lambda$ for which the system of linear equations $2xyz=12$, $x2y+z=4$ and $x+y+\lambda z=4$ has no solution is $2$ $2$ $3$ $3$
asked
May 11
in
Numerical Ability
by
akash.dinkar12
Boss
(
41.6k
points)

68
views
isi2018mma
engineeringmathematics
linearalgebra
systemofequations
+1
vote
1
answer
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
asked
May 7
in
Linear Algebra
by
Sayan Bose
Loyal
(
7.1k
points)

125
views
isi2019mma
engineeringmathematics
linearalgebra
0
votes
2
answers
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 $t$
asked
May 7
in
Linear Algebra
by
Sayan Bose
Loyal
(
7.1k
points)

155
views
isi2019mma
linearalgebra
engineeringmathematics
+1
vote
1
answer
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 $1$ $1$ $3$ $3$
asked
May 7
in
Linear Algebra
by
Sayan Bose
Loyal
(
7.1k
points)

138
views
isi2019mma
linearalgebra
systemofequations
0
votes
2
answers
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
in
Linear Algebra
by
Sayan Bose
Loyal
(
7.1k
points)

187
views
isi2019mma
engineeringmathematics
linearalgebra
+1
vote
0
answers
16
CSIR UGC NET
asked
Apr 28
in
Linear Algebra
by
Hirak
Active
(
3.4k
points)

47
views
linearalgebra
eigenvalue
matrices
+3
votes
1
answer
17
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______ $a,a,a$ $0,a,2a$ $a,2a,2a$ $a,a+\sqrt{2},a\sqrt{2}$
asked
Apr 25
in
Linear Algebra
by
Hirak
Active
(
3.4k
points)

92
views
engineeringmathematics
linearalgebra
eigenvalue
0
votes
0
answers
18
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
(
15.3k
points)

87
views
engineeringmathematics
linearalgebra
userisi2015
usermod
+3
votes
4
answers
19
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
by
Arjun
Veteran
(
420k
points)

1.9k
views
gate2019
engineeringmathematics
linearalgebra
determinant
+4
votes
3
answers
20
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
by
Arjun
Veteran
(
420k
points)

2.5k
views
gate2019
numericalanswers
engineeringmathematics
linearalgebra
eigenvalue
+2
votes
1
answer
21
Nullity of matrix
Nullity of a matrix = Total number columns – Rank of that matrix But how to calculate value of x when nullity is already given(1 in this case)
asked
Jan 24
in
Linear Algebra
by
Nandkishor3939
Active
(
1.3k
points)

145
views
engineeringmathematics
linearalgebra
matrices
rankofmatrix
matrix
0
votes
1
answer
22
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)

61
views
linearalgebra
engineeringmathematics
matrices
0
votes
1
answer
23
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
(
259
points)

136
views
linearalgebra
matrix
eigenvalue
0
votes
1
answer
24
MadeEasy Full Length Test 2019: Engineering Mathematics  Linear Algebra
asked
Jan 16
in
Linear Algebra
by
roman_1997
(
169
points)

92
views
linearalgebra
engineeringmathematics
madeeasytestseries2019
madeeasytestseries
0
votes
0
answers
25
Recurrence Relation for Array
A two dimensional array is stored in column major form in memory if the elements are stored in the following sequence ... calculated as the column number of the element we are looking for summing with the $row \times column$ number of elements. How does the above recurrence relation work?
asked
Jan 7
in
DS
by
kauray
(
209
points)

93
views
recurrence
recurrenceeqation
arrays
linearalgebra
operatingsystem
0
votes
0
answers
26
Doubt on syllabus
Is LU decomposition in course for GATE 2019?
asked
Jan 6
in
Linear Algebra
by
subho16
(
143
points)

55
views
engineeringmathematics
ludecomposition
linearalgebra
0
votes
0
answers
27
Eigen Values Doubt
Let there is a 2*2 Matrix and their eigen values are A and B. The eigen values of $(A+7I)^{1}$ ?
asked
Jan 4
in
Linear Algebra
by
Shamim Ahmed
Active
(
2.4k
points)

99
views
eigenvalue
engineeringmathematics
linearalgebra
0
votes
0
answers
28
The time complexity for the possible ways of multiplying the given set of n matrices.
asked
Jan 1
in
Algorithms
by
susgir2
Active
(
1.5k
points)

47
views
algorithms
timecomplexity
linearalgebra
0
votes
0
answers
29
doubt
how can we find factor of determinant by hit and trial method ? Please explain the steps https://gateoverflow.in/ask?cat=33
asked
Dec 26, 2018
in
Linear Algebra
by
Satbir
Boss
(
19.1k
points)

22
views
linearalgebra
0
votes
0
answers
30
Are proofs important at this time while I am preparing Engineering Mathematics?
Good Morning I am preparing Engineering Mathematics now and as the time is less, does proofs matters to learn? Thank you in Advance
asked
Dec 24, 2018
in
Mathematical Logic
by
sambana
(
45
points)

79
views
preparation
linearalgebra
discretemathematics
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Exam date is 1212020.
Where is this mentioned?
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