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Recent questions tagged matrix
1
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61
ISI 2021 | PCB CS | Question: 4
Let $A$ be a matrix of size row $\times$ col. $A$ has to be filled in a spiral clockwise fashion with successive integers from $1,2, \ldots$, row $\times$ col starting from the top left corner. For example, a $3 \times 4$ ... (int *)); for(i=0;i<row;i++){ A[i] = (int *)calloc(col,sizeof(int)); } spiralFill(A,row,col); }
admin
asked
in
Programming in C
Aug 8, 2022
by
admin
503
views
isi2021-pcb-cs
programming
programming-in-c
functions
matrix
descriptive
0
votes
1
answer
62
ISI 2020 | PCB Mathematics | Question: 3
Suppose $A$ is an $(n \times n)$ matrix over $\mathbb{R}$ such that $A^{p}=0$ for some positive integer $p$. Prove that $I+A$ is an invertible matrix, where $I$ is the $(n \times n)$ identity matrix. Find the characteristic polynomial of $A$.
admin
asked
in
Linear Algebra
Aug 8, 2022
by
admin
456
views
isi2020-pcb-mathematics
descriptive
linear-algebra
matrix
1
vote
1
answer
63
Eigen Values of an orthogonal matrix will always be +1 and the modulus will also be always |1|?
Eigen Values of an orthogonal matrix will always be +1 and the modulus will also be always |1|? I have a doubt on this point .
samarpita
asked
in
Linear Algebra
May 9, 2022
by
samarpita
9.0k
views
linear-algebra
eigen-value
matrix
18
votes
4
answers
64
GATE CSE 2022 | Question: 10
Consider the following two statements with respect to the matrices $\textit{A}_{m \times n}, \textit{B}_{n \times m}, \textit{C}_{n \times n}$ and $ \textit{D}_{n \times n}.$ Statement $1: tr \text{(AB)} = tr \text{(BA)}$ ... $2$ is correct. Both Statement $1$ and Statement $2$ are correct. Both Statement $1$ and Statement $2$ are wrong.
Arjun
asked
in
Linear Algebra
Feb 15, 2022
by
Arjun
10.4k
views
gatecse-2022
linear-algebra
matrix
1-mark
21
votes
5
answers
65
GATE CSE 2022 | Question: 35
Consider solving the following system of simultaneous equations using $\text{LU}$ decomposition. $x_{1} + x_{2} - 2x_{3} = 4$ $x_{1} + 3x_{2} - x_{3} = 7$ $2x_{1} + x_{2} - 5x_{3} = 7$ where $\textit{L}$ and $\textit{U}$ ... $\textit{L}_{32}= - \frac{1}{2}, \textit{U}_{33}= - \frac{1}{2}, x_{1}= 0$
Arjun
asked
in
Linear Algebra
Feb 15, 2022
by
Arjun
11.1k
views
gatecse-2022
linear-algebra
matrix
system-of-equations
2-marks
0
votes
1
answer
66
linear algebra - eigenvalues
What are the eigenvalues of the following matrix?
atulcse
asked
in
Linear Algebra
Jan 13, 2022
by
atulcse
395
views
linear-algebra
eigen-value
matrix
engineering-mathematics
1
vote
0
answers
67
Self doubt: what are eigen values of resultant matrix when add two matrices?
if eigen values of matrix A = a,b,c if eigen values of matrix B = x,y,z then is it holds every time that eigen value of A+B = a+x, b+y, c+z ? please give some reference to you answer, thankyou.
jaswanth431
asked
in
Linear Algebra
Dec 12, 2021
by
jaswanth431
250
views
engineering-mathematics
eigen-value
linear-algebra
matrix
2
votes
1
answer
68
Linear Algebra Eigenvalues
If the eigenvalues of a 3x3 matrix A are 1,2 and 3 then inverse of A is?
theakatsuki4
asked
in
Linear Algebra
Sep 16, 2021
by
theakatsuki4
4.7k
views
linear-algebra
engineering-mathematics
eigen-value
matrix
2
votes
1
answer
69
TIFR CSE 2021 | Part A | Question: 3
Let $M$ be an $n \times m$ real matrix. Consider the following: Let $k_{1}$ be the smallest number such that $M$ can be factorized as $A \cdot B$, where $A$ is an $n \times k_{1}$ and $B$ is a $k_{1} \times m$ matrix. Let $k_{2}$ be the smallest number ... $k_{1}= k_{2}= k_{3}$ No general relationship exists among $k_{1}, k_{2}$ and $k_{3}$
soujanyareddy13
asked
in
Linear Algebra
Mar 25, 2021
by
soujanyareddy13
629
views
tifr2021
linear-algebra
matrix
rank-of-matrix
3
votes
1
answer
70
TIFR CSE 2021 | Part B | Question: 8
Let $A$ and $B$ be two matrices of size $n \times n$ and with real-valued entries. Consider the following statements. If $AB = B$, then $A$ must be the identity matrix. If $A$ is an idempotent (i.e. $A^{2} = A$) nonsingular matrix, then $A$ must be the identity matrix. ... true of $A$? $1, 2 $ and $3$ Only $2$ and $3$ Only $1$ and $2$ Only $1$ and $3$ Only $2$
soujanyareddy13
asked
in
Linear Algebra
Mar 25, 2021
by
soujanyareddy13
658
views
tifr2021
linear-algebra
matrix
2
votes
1
answer
71
TIFR CSE 2021 | Part B | Question: 13
Let $A$ be a $3 \times 6$ matrix with real-valued entries. Matrix $A$ has rank $3$. We construct a graph with $6$ vertices where each vertex represents distinct column in $A$, and there is an edge between two vertices if the two columns represented ... is connected. There is a clique of size $3$. The graph has a cycle of length $4$. The graph is $3$-colourable.
soujanyareddy13
asked
in
Graph Theory
Mar 25, 2021
by
soujanyareddy13
578
views
tifr2021
graph-theory
graph-coloring
matrix
43
votes
14
answers
72
GATE CSE 2021 Set 2 | Question: 24
Suppose that $P$ is a $4 \times 5$ matrix such that every solution of the equation $\text{Px=0}$ is a scalar multiple of $\begin{bmatrix} 2 & 5 & 4 &3 & 1 \end{bmatrix}^T$. The rank of $P$ is __________
Arjun
asked
in
Linear Algebra
Feb 18, 2021
by
Arjun
18.1k
views
gatecse-2021-set2
numerical-answers
linear-algebra
matrix
rank-of-matrix
1-mark
16
votes
4
answers
73
GATE CSE 2021 Set 1 | Question: 52
Consider the following matrix.$\begin{pmatrix} 0 & 1 & 1 & 1\\ 1& 0& 1 & 1\\ 1& 1 & 0 & 1 \\1 & 1 & 1 & 0 \end{pmatrix}$The largest eigenvalue of the above matrix is __________.
Arjun
asked
in
Linear Algebra
Feb 18, 2021
by
Arjun
15.3k
views
gatecse-2021-set1
linear-algebra
matrix
eigen-value
numerical-answers
2-marks
2
votes
1
answer
74
CMI-2018-DataScience-A: 1
If $P$ is an invertible matrix and $A=PBP^{-1},$ then which of the following statements are necessarily true? $B=P^{-1}AP$ $|A|=|B|$ $A$ is invertible if and only if $B$ is invertible $B^T=A^T$
soujanyareddy13
asked
in
Others
Jan 29, 2021
by
soujanyareddy13
449
views
cmi2018-datascience
matrix
linear-algebra
0
votes
3
answers
75
CMI-2018-DataScience-A: 2
Let ... $|A|=|B|$ $|C|=|D|$ $|B|=-|C|$ $|A|=-|D|$
soujanyareddy13
asked
in
Others
Jan 29, 2021
by
soujanyareddy13
616
views
cmi2018-datascience
matrix
linear-algebra
2
votes
2
answers
76
CMI-2018-DataScience-A: 3
Let $x=\begin{bmatrix} 3& 1 & 2 \end{bmatrix}$. Which of the following statements are true? $x^Tx$ is a $3\times 3$ matrix $xx^T$ is a $3\times 3$ matrix $xx^T$ is a $1\times 1$ matrix $xx^T=x^Tx$
soujanyareddy13
asked
in
Others
Jan 29, 2021
by
soujanyareddy13
379
views
cmi2018-datascience
matrix
linear-algebra
discrete-mathematics
1
vote
1
answer
77
CMI-2018-DataScience-A: 4
A $n\times n$ matrix $A$ is said to be $symmetric$ if $A^T=A$. Suppose $A$ is an arbitrary $2\times 2$ matrix. Then which of the following matrices are symmetric (here $0$ denotes the $2\times 2$ matrix consisting of zeros): $A^TA$ $\begin{bmatrix} 0&A^T \\ A & 0 \end{bmatrix}$ $AA^T$ $\begin{bmatrix} A & 0 \\ 0 & A^T \end{bmatrix}$
soujanyareddy13
asked
in
Others
Jan 29, 2021
by
soujanyareddy13
549
views
cmi2018-datascience
matrix
linear-algebra
discrete-mathematics
0
votes
2
answers
78
CMI-2018-DataScience-B: 2
For numerical answers, the following forms are acceptable: fractions, decimals, symbolic e.g.:$\left( \begin{array}{c} n \\ r \end{array} \right)^n P_r , n!$ etc. Suppose $A,B$ and $C$ are $m\times m$ matrices. What does the following algorithm compute? (Here $A(i,j)$ ... .) for i=1 to m for j=1 to m for k=1 to m C(i,j)=A(i,k)*B(k,j)+C(i,j) end end end
soujanyareddy13
asked
in
Others
Jan 29, 2021
by
soujanyareddy13
333
views
cmi2018-datascience
matrix
linear-algebra
discrete-mathematics
0
votes
1
answer
79
CMI-2018-DataScience-B: 4
For numerical answers, the following forms are acceptable: fractions, decimals, symbolic e.g.:$\left( \begin{array}{c} n \\ r \end{array} \right)^n P_r , n!$ etc. In computing, a floating point operation (flop) is any one of the following operations ... . How does this number change if both the matrices are upper triangular?
soujanyareddy13
asked
in
Others
Jan 29, 2021
by
soujanyareddy13
335
views
cmi2018-datascience
matrix
linear-algebra
discrete-mathematics
0
votes
1
answer
80
CMI-2018-DataScience-B: 17
$\text{Description for the following question:}$ A golf club has $m$ members with serial numbers $1,2,\dots ,m$. If members with serial numbers $i$ and $j$ are friends, then $A(i,j)=A(j,i)=1,$ otherwise $A(i,j)=A(j,i)=0.$ By ... $1$ and member $2$ have at least one friend in common.
soujanyareddy13
asked
in
Others
Jan 29, 2021
by
soujanyareddy13
208
views
cmi2018-datascience
matrix
0
votes
1
answer
81
CMI-2018-DataScience-B: 18
$\text{Description for the following question:}$ A golf club has $m$ members with serial numbers $1,2,\dots ,m$. If members with serial numbers $i$ and $j$ are friends, then $A(i,j)=A(j,i)=1,$ otherwise $A(i,j)=A(j,i)=0.$ ... Then which of the following are necessarily true? Give reasons. $A^2(i,i)>0$ for all $i,\;1\underline< i \underline < m.$
soujanyareddy13
asked
in
Others
Jan 29, 2021
by
soujanyareddy13
239
views
cmi2018-datascience
matrix
0
votes
1
answer
82
CMI-2018-DataScience-B: 19
$\text{Description for the following question:}$ A golf club has $m$ members with serial numbers $1,2,\dots ,m$. If members with serial numbers $i$ and $j$ are friends, then $A(i,j)=A(j,i)=1,$ otherwise $A(i,j)=A(j,i)=0.$ ... $A^4(1,3)=0$. Then which of the following are necessarily true? Give reasons. $m\underline < 9$
soujanyareddy13
asked
in
Others
Jan 29, 2021
by
soujanyareddy13
173
views
cmi2018-datascience
matrix
0
votes
1
answer
83
CMI-2018-DataScience-B: 20
$\text{Description for the following question:}$ A golf club has $m$ members with serial numbers $1,2,\dots ,m$. If members with serial numbers $i$ and $j$ are friends, then $A(i,j)=A(j,i)=1,$ otherwise $A(i,j)=A(j,i)=0.$ ... $A^4(1,3)=0$. Then which of the following are necessarily true? Give reasons. $m\underline> 6$
soujanyareddy13
asked
in
Others
Jan 29, 2021
by
soujanyareddy13
197
views
cmi2018-datascience
matrix
1
vote
2
answers
84
CMI-2020-DataScience-B: 2
Consider the matrix $A=\begin{pmatrix} 0 & -1 \\ 1 & 0 \end{pmatrix}$. Find $A^n,$ in terms of $n,$ for $n\geq2.$
soujanyareddy13
asked
in
Linear Algebra
Jan 29, 2021
by
soujanyareddy13
553
views
cmi2020-datascience
linear-algebra
matrix
descriptive
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