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Recent questions tagged matrix
1
vote
1
answer
121
NIELIT 2017 DEC Scientist B - Section B: 60
Consider two matrices $M_1$ and $M_2$ with $M_1^*M_2=0$ and $M_1$ is non singular. Then which of the following is true? $M_2$ is non singular $M_2$ is null matrix $M_2$ is the identity matrix $M_2$ is transpose of $M_1$
admin
asked
in
Linear Algebra
Mar 30, 2020
by
admin
593
views
nielit2017dec-scientistb
engineering-mathematics
linear-algebra
matrix
13
votes
3
answers
122
GATE CSE 2020 | Question: 27
Let $A$ and $B$ be two $n \times n$ matrices over real numbers. Let rank($M$) and $\text{det}(M)$ denote the rank and determinant of a matrix $M$, respectively. Consider the following statements. $\text{rank}(AB) = \text{rank }(A) \text{rank }(B)$ ... Which of the above statements are TRUE? I and II only I and IV only II and III only III and IV only
Arjun
asked
in
Linear Algebra
Feb 12, 2020
by
Arjun
9.9k
views
gatecse-2020
linear-algebra
matrix
2-marks
1
vote
1
answer
123
TIFR CSE 2020 | Part A | Question: 5
Let $A$ be am $n\times n$ invertible matrix with real entries whose column sums are all equal to $1$. Consider the following statements: Every column in the matrix $A^{2}$ sums to $2$ Every column in the matrix $A^{3}$ sums to $3$ Every column in the matrix ... $(1)$ or $(2)$ all the $3$ statements $(1),(2),$ and $(3)$ are correct
admin
asked
in
Linear Algebra
Feb 10, 2020
by
admin
1.2k
views
tifr2020
engineering-mathematics
linear-algebra
matrix
3
votes
3
answers
124
ISI2014-DCG-8
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 $\begin{bmatrix}3 & 4 & 5 \end{bmatrix} M = \begin{bmatrix}0 & 1 & 0 \end{bmatrix}$ ... $\begin{bmatrix} -1 & 2 & 0 \end{bmatrix}$ $\begin{bmatrix} 9 & 10 & 8 \end{bmatrix}$
Arjun
asked
in
Linear Algebra
Sep 23, 2019
by
Arjun
764
views
isi2014-dcg
linear-algebra
matrix
3
votes
1
answer
125
ISI2014-DCG-38
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
Arjun
asked
in
Linear Algebra
Sep 23, 2019
by
Arjun
545
views
isi2014-dcg
linear-algebra
matrix
1
vote
1
answer
126
ISI2014-DCG-64
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 $3$ $1$ $0$ $-3$
Arjun
asked
in
Linear Algebra
Sep 23, 2019
by
Arjun
654
views
isi2014-dcg
linear-algebra
matrix
system-of-equations
0
votes
0
answers
127
ISI2014-DCG-70
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 $\begin{pmatrix} a^3 & a^3 \\ 0 & a^3 \end{pmatrix}$ ... $\begin{pmatrix} a^3 & 0 \\ 3a^3 & a^3 \end{pmatrix}$ $\begin{pmatrix} a^3 & 0 \\ -3a^3 & a^3 \end{pmatrix}$
Arjun
asked
in
Linear Algebra
Sep 23, 2019
by
Arjun
382
views
isi2014-dcg
linear-algebra
matrix
inverse
0
votes
0
answers
128
ISI2015-MMA-38
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
Arjun
asked
in
Linear Algebra
Sep 23, 2019
by
Arjun
579
views
isi2015-mma
linear-algebra
matrix
7
votes
3
answers
129
ISI2015-MMA-39
The eigenvalues of the matrix $X = \begin{pmatrix} 2 & 1 & 1 \\ 1 & 2 & 1 \\ 1 & 1 & 2 \end{pmatrix}$ are $1,1,4$ $1,4,4$ $0,1,4$ $0,4,4$
Arjun
asked
in
Linear Algebra
Sep 23, 2019
by
Arjun
1.1k
views
isi2015-mma
linear-algebra
matrix
eigen-value
0
votes
0
answers
130
ISI2015-MMA-40
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 $3$
Arjun
asked
in
Linear Algebra
Sep 23, 2019
by
Arjun
591
views
isi2015-mma
linear-algebra
matrix
rank-of-matrix
2
votes
2
answers
131
ISI2015-MMA-42
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 $\lambda_1+\lambda_2+\lambda_3 = \sqrt{2}+1$ ... $\{ - \frac{\pi}{4}, \frac{\pi}{4} \}$ $\{ - \frac{\pi}{3}, \frac{\pi}{3} \}$
Arjun
asked
in
Linear Algebra
Sep 23, 2019
by
Arjun
766
views
isi2015-mma
linear-algebra
matrix
eigen-value
2
votes
1
answer
132
ISI2015-MMA-61
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 $A=CB$
Arjun
asked
in
Linear Algebra
Sep 23, 2019
by
Arjun
576
views
isi2015-mma
linear-algebra
matrix
2
votes
1
answer
133
ISI2015-MMA-62
If the matrix $A = \begin{bmatrix} a & 1 \\ 2 & 3 \end{bmatrix}$ has $1$ as an eigenvalue, then $\textit{trace}(A)$ is $4$ $5$ $6$ $7$
Arjun
asked
in
Linear Algebra
Sep 23, 2019
by
Arjun
849
views
isi2015-mma
linear-algebra
matrix
eigen-value
1
vote
2
answers
134
ISI2015-MMA-63
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 $A^{2010}$ ... $\begin{pmatrix} 0 & 1 \\ -1 & 0 \end{pmatrix}$
Arjun
asked
in
Linear Algebra
Sep 23, 2019
by
Arjun
651
views
isi2015-mma
linear-algebra
matrix
0
votes
1
answer
135
ISI2015-DCG-5
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
gatecse
asked
in
Linear Algebra
Sep 18, 2019
by
gatecse
465
views
isi2015-dcg
linear-algebra
matrix
2
votes
1
answer
136
ISI2015-DCG-31
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 $\mid A \mid =1$ $\mid A \mid =0 \text{ or } 1$ $\mid A \mid =-1, 0 \text{ or } 1$ $\mid A \mid =-1 \text{ or } 1$
gatecse
asked
in
Linear Algebra
Sep 18, 2019
by
gatecse
426
views
isi2015-dcg
linear-algebra
matrix
determinant
0
votes
1
answer
137
ISI2015-DCG-32
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
gatecse
asked
in
Linear Algebra
Sep 18, 2019
by
gatecse
974
views
isi2015-dcg
linear-algebra
matrix
eigen-vectors
1
vote
1
answer
138
ISI2015-DCG-33
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 $n$. $AB-BA$ $\begin{pmatrix} A & O \\ O & B \end{pmatrix}$ $\begin{pmatrix} A & I \\ I & B \end{pmatrix}$ $A^2 – B^2$
gatecse
asked
in
Linear Algebra
Sep 18, 2019
by
gatecse
493
views
isi2015-dcg
linear-algebra
matrix
orthogonal-matrix
1
vote
1
answer
139
ISI2015-DCG-34
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 $\mid A_{ji} \mid =0$
gatecse
asked
in
Linear Algebra
Sep 18, 2019
by
gatecse
339
views
isi2015-dcg
linear-algebra
matrix
determinant
0
votes
1
answer
140
ISI2016-DCG-4
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
gatecse
asked
in
Linear Algebra
Sep 18, 2019
by
gatecse
341
views
isi2016-dcg
linear-algebra
matrix
1
vote
1
answer
141
ISI2016-DCG-31
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 $\mid\:(A)\mid=1$ $\mid\:(A)\mid=0\:\text{or}\:1$ $\mid\:(A)\mid=-1,0\:\text{or}\:1$ $\mid\:(A)\mid=-1\:\text{or}\:1$
gatecse
asked
in
Linear Algebra
Sep 18, 2019
by
gatecse
383
views
isi2016-dcg
linear-algebra
matrix
determinant
0
votes
0
answers
142
ISI2016-DCG-32
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
gatecse
asked
in
Linear Algebra
Sep 18, 2019
by
gatecse
312
views
isi2016-dcg
linear-algebra
matrix
orthogonal-matrix
eigen-vectors
0
votes
0
answers
143
ISI2016-DCG-33
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 $n.$ $AB-BA$ $\begin{pmatrix} A & O \\ O & B \end{pmatrix}$ $\begin{pmatrix} A & I \\ I & B \end{pmatrix}$ $A^{2}-B^{2}$
gatecse
asked
in
Linear Algebra
Sep 18, 2019
by
gatecse
253
views
isi2016-dcg
linear-algebra
matrix
orthogonal-matrix
0
votes
0
answers
144
ISI2016-DCG-34
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 $\mid A_{ji}\mid=0.$
gatecse
asked
in
Linear Algebra
Sep 18, 2019
by
gatecse
291
views
isi2016-dcg
linear-algebra
matrix
minors
1
vote
1
answer
145
ISI2017-DCG-4
If $A$ is a $3 \times 3$ matrix satisfying $A^3 – A^2 +A-I= O$ (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
gatecse
asked
in
Linear Algebra
Sep 18, 2019
by
gatecse
444
views
isi2017-dcg
linear-algebra
matrix
2
votes
2
answers
146
ISI2018-DCG-16
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 $(1,-1)$ $(1,0)$ $(-1,-1)$ $(0,1)$
gatecse
asked
in
Linear Algebra
Sep 18, 2019
by
gatecse
499
views
isi2018-dcg
linear-algebra
matrix
inverse
3
votes
4
answers
147
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?
srestha
asked
in
Linear Algebra
Jun 1, 2019
by
srestha
2.5k
views
discrete-mathematics
matrix
0
votes
1
answer
148
Self-Doubt: 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?
srestha
asked
in
Linear Algebra
May 27, 2019
by
srestha
1.3k
views
engineering-mathematics
linear-algebra
matrix
1
vote
1
answer
149
ISI2018-PCB-A1
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 $A^2=A$.
akash.dinkar12
asked
in
Linear Algebra
May 12, 2019
by
akash.dinkar12
519
views
isi2018-pcb-a
engineering-mathematics
linear-algebra
matrix
descriptive
1
vote
1
answer
150
ISI2019-MMA-23
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 skew-symmetric matrix None of the above must necessarily hold
Sayan Bose
asked
in
Linear Algebra
May 7, 2019
by
Sayan Bose
1.7k
views
isi2019-mma
engineering-mathematics
linear-algebra
matrix
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