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Recent questions tagged matrices
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1
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
asked
Sep 23
in
Linear Algebra
by
Arjun
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423k
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11
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isi2014dcg
linearalgebra
matrices
realmatrix
0
votes
0
answers
2
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 $3$ $1$ $0$ $3$
asked
Sep 23
in
Linear Algebra
by
Arjun
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423k
points)

22
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isi2014dcg
linearalgebra
matrices
systemofequations
0
votes
0
answers
3
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
in
Linear Algebra
by
Arjun
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423k
points)

13
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isi2014dcg
linearalgebra
matrices
inverse
0
votes
0
answers
4
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
in
Linear Algebra
by
Arjun
Veteran
(
423k
points)

7
views
isi2015mma
linearalgebra
matrices
0
votes
1
answer
5
ISI2015MMA39
The eigenvalues of the matrix $X = \begin{pmatrix} 2 & 1 & 1 \\ 1 & 2 & 1 \\ 1 & 1 & 2 \end{pmatrix}$ are $1,1,4$ $1,4,4$ $0,1,4$ $0,4,4$
asked
Sep 23
in
Linear Algebra
by
Arjun
Veteran
(
423k
points)

11
views
isi2015mma
linearalgebra
matrices
eigenvalue
0
votes
0
answers
6
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
in
Linear Algebra
by
Arjun
Veteran
(
423k
points)

12
views
isi2015mma
linearalgebra
matrices
rankofmatrix
0
votes
0
answers
7
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
in
Linear Algebra
by
Arjun
Veteran
(
423k
points)

11
views
isi2015mma
linearalgebra
matrices
eigenvalue
0
votes
1
answer
8
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 $A=CB$
asked
Sep 23
in
Linear Algebra
by
Arjun
Veteran
(
423k
points)

8
views
isi2015mma
linearalgebra
matrices
0
votes
1
answer
9
ISI2015MMA62
If the matrix $A = \begin{bmatrix} a & 1 \\ 2 & 3 \end{bmatrix}$ has $1$ as an eigenvalue, then $\textit{trace}(A)$ is $4$ $5$ $6$ $7$
asked
Sep 23
in
Linear Algebra
by
Arjun
Veteran
(
423k
points)

11
views
isi2015mma
linearalgebra
matrices
eigenvalue
0
votes
1
answer
10
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 $A^{2010}$ ... $\begin{pmatrix} 0 & 1 \\ 1 & 0 \end{pmatrix}$
asked
Sep 23
in
Linear Algebra
by
Arjun
Veteran
(
423k
points)

9
views
isi2015mma
linearalgebra
matrices
trigonometry
0
votes
1
answer
11
ISI2015DCG5
If $f(x) = \begin{bmatrix} \cos x & \sin x & 0 \\ \sin x & \cos x & 0 \\ 0 & 0 & 1 \end{bmatrix}$ then the value of $\big(f(x)\big)^2$ is $f(x)$ $f(2x)$ $2f(x)$ None of these
asked
Sep 18
in
Linear Algebra
by
gatecse
Boss
(
16.6k
points)

23
views
isi2015dcg
linearalgebra
matrices
0
votes
1
answer
12
ISI2015DCG31
Let $A$ be an $n \times n$ matrix such that $\mid A^{2} \mid\: =1$. Here $\mid A \mid $ stands for determinant of matrix $A$. Then $\mid A \mid =1$ $\mid A \mid =0 \text{ or } 1$ $\mid A \mid =1, 0 \text{ or } 1$ $\mid A \mid =1 \text{ or } 1$
asked
Sep 18
in
Linear Algebra
by
gatecse
Boss
(
16.6k
points)

17
views
isi2015dcg
linearalgebra
matrices
determinant
0
votes
1
answer
13
ISI2015DCG32
The set of vectors constituting an orthogonal basis in $\mathbb{R} ^3$ is $\begin{Bmatrix} \begin{pmatrix} 1 \\ 1 \\ 0 \end{pmatrix}, & \begin{pmatrix} 1 \\ 1 \\ 0 \end{pmatrix}, & \begin{pmatrix} 0 \\ 0 \\ 1 \end{pmatrix} \end{Bmatrix}$ ... None of these
asked
Sep 18
in
Linear Algebra
by
gatecse
Boss
(
16.6k
points)

40
views
isi2015dcg
linearalgebra
matrices
eigenvectors
0
votes
1
answer
14
ISI2015DCG33
Suppose $A$ and $B$ are orthogonal $n \times n$ matrices. Which of the following is also an orthogonal matrix? Assume that $O$ is the null matrix of order $n \times n$ and $I$ is the identity matrix of order $n$. $ABBA$ $\begin{pmatrix} A & O \\ O & B \end{pmatrix}$ $\begin{pmatrix} A & I \\ I & B \end{pmatrix}$ $A^2 – B^2$
asked
Sep 18
in
Linear Algebra
by
gatecse
Boss
(
16.6k
points)

11
views
isi2015dcg
linearalgebra
matrices
orthogonalmatrix
0
votes
1
answer
15
ISI2015DCG34
Let $A_{ij}$ denote the minors of an $n \times n$ matrix $A$. What is the relationship between $\mid A_{ij} \mid $ and $\mid A_{ji} \mid $? They are always equal $\mid A_{ij} \mid = – \mid A _{ji} \mid \text{ if } i \neq j$ They are equal if $A$ is a symmetric matrix If $\mid A_{ij} \mid =0$ then $\mid A_{ji} \mid =0$
asked
Sep 18
in
Linear Algebra
by
gatecse
Boss
(
16.6k
points)

11
views
isi2015dcg
linearalgebra
matrices
determinant
0
votes
1
answer
16
ISI2017DCG4
If $A$ is a $3 \times 3$ matrix satisfying $A^3 – A^2 +AI= O$ (where $O$ is the zero matrix and $I$ is the identity matrix) then the value of $A^4$ is $A$ $O$ $I$ none of these
asked
Sep 18
in
Linear Algebra
by
gatecse
Boss
(
16.6k
points)

9
views
isi2017dcg
linearalgebra
matrices
nullmatrix
identitymatrix
+1
vote
1
answer
17
CMI2019B6
Let $A$ be an $n\times n $ matrix of integers such that each row and each column is arranged in ascending order. We want to check whether a number $k$ appears in $A.$ If $k$ is present, we should report its position  that is, the row $i$ and ... $A.$ Justify the complexity of your algorithm. For both algorithms, describe a worstcase input where $k$ is present in $A.$
asked
Sep 13
in
Algorithms
by
gatecse
Boss
(
16.6k
points)

13
views
cmi2019
algorithms
matrices
descriptive
poof
nongate
0
votes
2
answers
18
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
(
117k
points)

169
views
discretemathematics
linearalgebra
matrix
matrices
0
votes
1
answer
19
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
(
117k
points)

140
views
engineeringmathematics
linearalgebra
matrices
+1
vote
1
answer
20
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
(
41.8k
points)

68
views
isi2018pcba
engineeringmathematics
linearalgebra
matrices
descriptive
+1
vote
0
answers
21
CSIR UGC NET
asked
Apr 28
in
Linear Algebra
by
Hirak
Active
(
3.5k
points)

51
views
linearalgebra
eigenvalue
matrices
+2
votes
1
answer
22
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)

153
views
engineeringmathematics
linearalgebra
matrices
rankofmatrix
matrix
0
votes
1
answer
23
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)

63
views
linearalgebra
engineeringmathematics
matrices
+1
vote
0
answers
24
#set theory #groups
Consider the set H of all 3 × 3 matrices of the type: $\begin{bmatrix} a&f&e\\ 0&b&d\\ 0&0&c\\ \end{bmatrix}$ where a, b, c, d, e and f are real numbers and $abc ≠ 0$. Under the matrix multiplication operation, the set H is: (a) a group (b) a monoid but not a group (c) a semigroup but not a monoid (d) neither a group nor a semigroup
asked
Jan 5
in
Set Theory & Algebra
by
Kunal Kadian
Active
(
2.8k
points)

70
views
settheory&algebra
groups
matrices
0
votes
0
answers
25
Determinant
True and false IF A is 5*5 matrix then det(4$A^{3}$)=$4^{5}det(A^{3}))$ det($(4A)^{3}$)=$det(4^{3}A^{3}))$ i think both are true ??
asked
Jan 4
in
Mathematical Logic
by
Gurdeep Saini
Boss
(
10.2k
points)

54
views
engineeringmathematics
matrices
easy
+2
votes
1
answer
26
Cases when LU decomposition is possible.
I had already visited below link but was unable to grasp it. https://math.stackexchange.com/questions/218770/whendoesasquarematrixhaveanludecomposition. I made some form of selfanalysis, let me know if I am in the correct ... pivot, and if such cannot be fixed without a row shuffle operation, then LU decomposition is not possible. Am I correct?
asked
Nov 18, 2018
in
Linear Algebra
by
Ayush Upadhyaya
Boss
(
27.2k
points)

248
views
linearalgebra
matrices
+1
vote
0
answers
27
Zeal Test Series 2019: Linear Algebra  Matrices
asked
Nov 17, 2018
in
Linear Algebra
by
Prince Sindhiya
Loyal
(
5.6k
points)

78
views
zeal
linearalgebra
discretemathematics
matrices
zeal2019
0
votes
0
answers
28
Virtual Gate Test Series: Linear Algebra  Eigen Value
asked
Oct 16, 2018
in
Linear Algebra
by
Prince Sindhiya
Loyal
(
5.6k
points)

57
views
engineeringmathematics
linearalgebra
matrices
eigenvalue
virtualgatetestseries
0
votes
0
answers
29
Virtual Gate Test Series: Linear Algebra  Eigen Values of a Unity Matrix
asked
Oct 15, 2018
in
Linear Algebra
by
Prince Sindhiya
Loyal
(
5.6k
points)

81
views
engineeringmathematics
linearalgebra
matrices
eigenvalue
virtualgatetestseries
+4
votes
5
answers
30
Eigen Value
An orthogonal matrix A has eigen values 1, 2 and 4. What is the trace of the matrix
asked
Sep 20, 2018
in
Linear Algebra
by
aditi19
Active
(
5k
points)

285
views
matrices
eigenvalue
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