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Recent questions tagged matrices
+1
vote
3
answers
1
ISI2014DCG8
If $M$ is a $3 \times 3$ matrix such that $\begin{bmatrix} 0 & 1 & 2 \end{bmatrix}M=\begin{bmatrix}1 & 0 & 0 \end{bmatrix}$ and $\begin{bmatrix}3 & 4 & 5 \end{bmatrix} M = \begin{bmatrix}0 & 1 & 0 \end{bmatrix}$ ... $\begin{bmatrix} 1 & 2 & 0 \end{bmatrix}$ $\begin{bmatrix} 9 & 10 & 8 \end{bmatrix}$
asked
Sep 23, 2019
in
Linear Algebra
by
Arjun
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(
431k
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118
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isi2014dcg
linearalgebra
matrices
+1
vote
1
answer
2
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, 2019
in
Linear Algebra
by
Arjun
Veteran
(
431k
points)

59
views
isi2014dcg
linearalgebra
matrices
0
votes
1
answer
3
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, 2019
in
Linear Algebra
by
Arjun
Veteran
(
431k
points)

59
views
isi2014dcg
linearalgebra
matrices
systemofequations
0
votes
0
answers
4
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, 2019
in
Linear Algebra
by
Arjun
Veteran
(
431k
points)

40
views
isi2014dcg
linearalgebra
matrices
inverse
0
votes
0
answers
5
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, 2019
in
Linear Algebra
by
Arjun
Veteran
(
431k
points)

27
views
isi2015mma
linearalgebra
matrices
+2
votes
2
answers
6
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, 2019
in
Linear Algebra
by
Arjun
Veteran
(
431k
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81
views
isi2015mma
linearalgebra
matrices
eigenvalue
0
votes
0
answers
7
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, 2019
in
Linear Algebra
by
Arjun
Veteran
(
431k
points)

37
views
isi2015mma
linearalgebra
matrices
rankofmatrix
0
votes
0
answers
8
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, 2019
in
Linear Algebra
by
Arjun
Veteran
(
431k
points)

44
views
isi2015mma
linearalgebra
matrices
eigenvalue
+1
vote
1
answer
9
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, 2019
in
Linear Algebra
by
Arjun
Veteran
(
431k
points)

40
views
isi2015mma
linearalgebra
matrices
0
votes
1
answer
10
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, 2019
in
Linear Algebra
by
Arjun
Veteran
(
431k
points)

51
views
isi2015mma
linearalgebra
matrices
eigenvalue
0
votes
1
answer
11
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, 2019
in
Linear Algebra
by
Arjun
Veteran
(
431k
points)

26
views
isi2015mma
linearalgebra
matrices
0
votes
1
answer
12
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, 2019
in
Linear Algebra
by
gatecse
Boss
(
17.5k
points)

40
views
isi2015dcg
linearalgebra
matrices
0
votes
1
answer
13
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, 2019
in
Linear Algebra
by
gatecse
Boss
(
17.5k
points)

35
views
isi2015dcg
linearalgebra
matrices
determinant
0
votes
1
answer
14
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, 2019
in
Linear Algebra
by
gatecse
Boss
(
17.5k
points)

57
views
isi2015dcg
linearalgebra
matrices
eigenvectors
0
votes
1
answer
15
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, 2019
in
Linear Algebra
by
gatecse
Boss
(
17.5k
points)

25
views
isi2015dcg
linearalgebra
matrices
orthogonalmatrix
0
votes
1
answer
16
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, 2019
in
Linear Algebra
by
gatecse
Boss
(
17.5k
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26
views
isi2015dcg
linearalgebra
matrices
determinant
0
votes
1
answer
17
ISI2016DCG4
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, 2019
in
Linear Algebra
by
gatecse
Boss
(
17.5k
points)

22
views
isi2016dcg
linearalgebra
matrices
+1
vote
1
answer
18
ISI2016DCG31
Let $A$ be an $n\times n$ matrix such that $\mid\: A^{2}\mid=1.\:\: \mid A\:\mid$ 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, 2019
in
Linear Algebra
by
gatecse
Boss
(
17.5k
points)

23
views
isi2016dcg
linearalgebra
matrices
determinant
0
votes
0
answers
19
ISI2016DCG32
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, 2019
in
Linear Algebra
by
gatecse
Boss
(
17.5k
points)

13
views
isi2016dcg
linearalgebra
matrices
orthogonalmatrix
eigenvectors
0
votes
0
answers
20
ISI2016DCG33
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, 2019
in
Linear Algebra
by
gatecse
Boss
(
17.5k
points)

14
views
isi2016dcg
linearalgebra
matrices
orthogonalmatrix
0
votes
0
answers
21
ISI2016DCG34
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. $\mid A_{ij}\mid=\mid A_{ji}\mid$ 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, 2019
in
Linear Algebra
by
gatecse
Boss
(
17.5k
points)

13
views
isi2016dcg
linearalgebra
matrices
minors
0
votes
1
answer
22
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, 2019
in
Linear Algebra
by
gatecse
Boss
(
17.5k
points)

24
views
isi2017dcg
linearalgebra
matrices
+1
vote
1
answer
23
ISI2018DCG16
Let $A=\begin{pmatrix} 1 & 1 & 0\\ 0 & a & b\\1 & 0 & 1 \end{pmatrix}$. Then $A^{1}$ does not exist if $(a,b)$ is equal to $(1,1)$ $(1,0)$ $(1,1)$ $(0,1)$
asked
Sep 18, 2019
in
Linear Algebra
by
gatecse
Boss
(
17.5k
points)

28
views
isi2018dcg
linearalgebra
matrices
inverse
0
votes
2
answers
24
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, 2019
in
Linear Algebra
by
srestha
Veteran
(
119k
points)

217
views
discretemathematics
linearalgebra
matrices
+2
votes
4
answers
25
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, 2019
in
Linear Algebra
by
srestha
Veteran
(
119k
points)

310
views
discretemathematics
matrices
0
votes
1
answer
26
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, 2019
in
Linear Algebra
by
srestha
Veteran
(
119k
points)

166
views
engineeringmathematics
linearalgebra
matrices
+1
vote
1
answer
27
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, 2019
in
Linear Algebra
by
akash.dinkar12
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(
42.5k
points)

88
views
isi2018pcba
engineeringmathematics
linearalgebra
matrices
descriptive
+1
vote
1
answer
28
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, 2019
in
Linear Algebra
by
Sayan Bose
Loyal
(
7.4k
points)

149
views
isi2019mma
engineeringmathematics
linearalgebra
matrices
0
votes
2
answers
29
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, 2019
in
Linear Algebra
by
Sayan Bose
Loyal
(
7.4k
points)

172
views
isi2019mma
linearalgebra
engineeringmathematics
matrices
+1
vote
0
answers
30
CSIR UGC NET
asked
Apr 28, 2019
in
Linear Algebra
by
Hirak
Active
(
3.6k
points)

61
views
linearalgebra
eigenvalue
matrices
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