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Recent questions tagged linear-algebra
3
votes
1
answer
61
#self doubt
How to solve this question?
samarpita
asked
in
Linear Algebra
Dec 28, 2021
by
samarpita
268
views
linear-algebra
eigen-value
1
vote
0
answers
62
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
138
views
engineering-mathematics
eigen-value
linear-algebra
matrix
0
votes
1
answer
63
CMI-2021-Data Science
rsansiya111
asked
in
Linear Algebra
Dec 9, 2021
by
rsansiya111
154
views
linear-algebra
1
vote
0
answers
64
CMI-2021 Data Science
Which of the following statement(s) is/are true for an arbitrary n × n matrix A? (a) Exchanging two rows of A does not change its determinant. (b) Exchanging two rows of A does not change its trace. (c) Replacing each diagonal element of A with a 1 does not change its determinant. (d) Exchanging two columns of A negates its determinant.
rsansiya111
asked
in
Linear Algebra
Dec 9, 2021
by
rsansiya111
168
views
linear-algebra
0
votes
0
answers
65
NPTEL Assignment Question
Check whether the following set of vectors are linearly dependent or independent. (a) S = {(1, 2, −2, −1),(2, 1, −1, 4),(−3, 0, 3, −2)} (b) S = {(1, 3, −2, 5, 4),(1, 4, 1, 3, 5),(1, 4, 2, 4, 3),(2, 7, −3, 6, 13)}
rsansiya111
asked
in
Linear Algebra
Dec 6, 2021
by
rsansiya111
159
views
linear-algebra
0
votes
0
answers
66
NPTEL Assignment Question
Show that the set F = ({1, 0}, +, .) is a field where + and . are defined as 1+1=0, 0+0=0, 0+1=1+0=1, 0.0=0.1=1.0=0, 1.1=1.
rsansiya111
asked
in
Linear Algebra
Dec 6, 2021
by
rsansiya111
182
views
linear-algebra
2
votes
1
answer
67
Applied Grand Test 2
What is the value of the given determinant ?
LRU
asked
in
Linear Algebra
Nov 22, 2021
by
LRU
429
views
linear-algebra
test-series
determinant
4
votes
4
answers
68
Applied Test Series
Consider the system of equations x+y+z=3 x+2y+3z=4 x+4y+kz=6 The above system of equations will not have a unique solution for k equals to___
LRU
asked
in
Linear Algebra
Nov 5, 2021
by
LRU
405
views
test-series
engineering-mathematics
linear-algebra
system-of-equations
2
votes
1
answer
69
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
2.6k
views
linear-algebra
engineering-mathematics
eigen-value
matrix
2
votes
1
answer
70
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
359
views
tifr2021
linear-algebra
matrix
rank-of-matrix
3
votes
1
answer
71
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
266
views
tifr2021
linear-algebra
matrix
20
votes
6
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
8.0k
views
gatecse-2021-set2
numerical-answers
linear-algebra
matrix
rank-of-matrix
1-mark
10
votes
2
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
6.3k
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
316
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
361
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
264
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
316
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
204
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
201
views
cmi2018-datascience
matrix
linear-algebra
discrete-mathematics
1
vote
2
answers
80
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
379
views
cmi2020-datascience
linear-algebra
matrix
descriptive
1
vote
3
answers
81
NIELIT 2016 MAR Scientist C - Section B: 3
The matrices $\begin{bmatrix} \cos\theta &-\sin \theta \\ \sin \theta & cos \theta \end{bmatrix}$ and $\begin{bmatrix} a & 0 \\ 0 & b \end{bmatrix}$ commute under the multiplication if $a=b \text{(or)} \theta =n\pi, \: n$ is an integer always never if $a\cos \theta \neq b\sin \theta$
Lakshman Patel RJIT
asked
in
Linear Algebra
Apr 2, 2020
by
Lakshman Patel RJIT
449
views
nielit2016mar-scientistc
linear-algebra
matrix
0
votes
2
answers
82
NIELIT 2016 MAR Scientist C - Section B: 8
The eigenvalues of the matrix $\begin{bmatrix}1 & 2\\ 4 & 3 \end{bmatrix}$ are $\text{5 and -5}$ $\text{5 and -1}$ $\text{1 and -5}$ $\text{2 and 3}$
Lakshman Patel RJIT
asked
in
Linear Algebra
Apr 2, 2020
by
Lakshman Patel RJIT
365
views
nielit2016mar-scientistc
engineering-mathematics
linear-algebra
0
votes
1
answer
83
NIELIT 2016 MAR Scientist C - Section B: 9
Consider three vectors $x=\begin{bmatrix}1\\2 \end{bmatrix}, y=\begin{bmatrix}4\\8 \end{bmatrix},z=\begin{bmatrix}3\\1 \end{bmatrix}$. Which of the folowing statements is true $x$ and $y$ are linearly independent $x$ and $y$ are linearly dependent $x$ and $z$ are linearly dependent $y$ and $z$ are linearly dependent
Lakshman Patel RJIT
asked
in
Linear Algebra
Apr 2, 2020
by
Lakshman Patel RJIT
288
views
nielit2016mar-scientistc
engineering-mathematics
linear-algebra
0
votes
0
answers
84
NIELIT 2016 MAR Scientist C - Section B: 19
If product of matrix $A=\begin{bmatrix}\cos^{2}\theta &\cos \theta \sin \theta \\ \cos \theta \sin \theta &\sin ^{2} \theta& \end{bmatrix}$ ... by an odd multiple of $\pi$ even multiple of $\pi$ odd multiple of $\dfrac{\pi}{2}$ even multiple of $\dfrac{\pi}{2}$
Lakshman Patel RJIT
asked
in
Linear Algebra
Apr 2, 2020
by
Lakshman Patel RJIT
331
views
nielit2016mar-scientistc
linear-algebra
matrix
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