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Recent questions and answers in Linear Algebra
2
votes
1
answer
1
Applied Grand Test 2
What is the value of the given determinant ?
Ratul Chatterjee
answered
in
Linear Algebra
Jul 20
by
Ratul Chatterjee
345
views
linear-algebra
test-series
determinant
1
vote
1
answer
2
GATE-2014 EC
Which one of the following statements is NOT true for a square matrix A? If A is real symmetric, the eigen values of A are the diagonal elements of it. If all the principal minors of A are positive, all the eigen values of A are also positive. My question is what is “principal minors of A” ?
ankitgupta.1729
answered
in
Linear Algebra
May 10
by
ankitgupta.1729
132
views
linear-algebra
gate2014-ec-1
eigen-value
1
vote
1
answer
3
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 .
Bharat Bhushan
answered
in
Linear Algebra
May 9
by
Bharat Bhushan
524
views
linear-algebra
eigen-value
matrix
33
votes
3
answers
4
GATE CSE 2014 Set 3 | Question: 4
Which one of the following statements is TRUE about every $n \times n$ matrix with only real eigenvalues? If the trace of the matrix is positive and the determinant of the matrix is negative, at least one of its eigenvalues is ... eigenvalues are positive. If the product of the trace and determinant of the matrix is positive, all its eigenvalues are positive.
This_is_Nimishka
answered
in
Linear Algebra
Apr 27
by
This_is_Nimishka
8.5k
views
gatecse-2014-set3
linear-algebra
eigen-value
normal
27
votes
5
answers
5
GATE CSE 2012 | Question: 11
Let A be the $ 2 × 2 $ matrix with elements $a_{11} = a_{12} = a_{21} = +1 $ and $ a_{22} = −1 $ . Then the eigenvalues of the matrix $A^{19}$ are $1024$ and $−1024$ $1024\sqrt{2}$ and $−1024 \sqrt{2}$ $4 \sqrt{2}$ and $−4 \sqrt{2}$ $512 \sqrt{2}$ and $−512 \sqrt{2}$
This_is_Nimishka
answered
in
Linear Algebra
Apr 26
by
This_is_Nimishka
8.0k
views
gatecse-2012
linear-algebra
eigen-value
3
votes
3
answers
6
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 $\textit{U}$ ... $\textit{L}_{32}= - \frac{1}{2}, \textit{U}_{33}= - \frac{1}{2}, x_{1}= 0$
Argharupa Adhikary
answered
in
Linear Algebra
Apr 25
by
Argharupa Adhikary
1.1k
views
gatecse-2022
linear-algebra
matrix
3
votes
2
answers
7
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.
s_dr_13
answered
in
Linear Algebra
Apr 9
by
s_dr_13
1.2k
views
gatecse-2022
linear-algebra
matrix
17
votes
6
answers
8
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 __________
0xprateek
answered
in
Linear Algebra
Mar 23
by
0xprateek
7.1k
views
gatecse-2021-set2
numerical-answers
linear-algebra
matrix
rank-of-matrix
30
votes
4
answers
9
GATE CSE 2004 | Question: 76
In an $M \times N$ matrix all non-zero entries are covered in $a$ rows and $b$ columns. Then the maximum number of non-zero entries, such that no two are on the same row or column, is $\leq a +b$ $\leq \max(a, b)$ $\leq \min(M-a, N-b)$ $\leq \min(a, b)$
0xprateek
answered
in
Linear Algebra
Mar 1
by
0xprateek
6.9k
views
gatecse-2004
linear-algebra
normal
matrix
1
vote
2
answers
10
eigen values and determinents
Let A be a 4 × 4 matrix with real entries such that -1, 1, 2, -2 are its eigen values. If B = A4 - 5A2 + 5I where I denotes 4 × 4 identity matrix, then which of the following is correct? (det(X) represents determinant of X) (A) det(A + B) = 0 (B) det(B) = 1 (C) trace of A + B is 4 (D) all of these
preeti0448
answered
in
Linear Algebra
Feb 28
by
preeti0448
1.0k
views
eigen-value
engineering-mathematics
linear-algebra
1
vote
1
answer
11
GATE CSE 2022 | Question: 43
Which of the following is/are the eigenvector(s) for the matrix given below? $\begin{pmatrix} - 9 & - 6 & - 2 & - 4 \\ - 8 & - 6 & - 3 & - 1 \\ 20 & 15 & 8 & 5 \\ 32 & 21 & 7 & 12 \end{pmatrix}$ ... $\begin{pmatrix} - 1 \\ 0 \\ 2 \\ 2 \end{pmatrix}$ $\begin{pmatrix} 0 \\ 1 \\ - 3 \\ 0 \end{pmatrix}$
Sachin Mittal 1
answered
in
Linear Algebra
Feb 15
by
Sachin Mittal 1
1.1k
views
gatecse-2022
linear-algebra
eigen-value
multiple-selects
0
votes
0
answers
12
(Solved now) Gateoverflow test doubt
In this question – https://gateoverflow.in/348646/Gate-overflow-linear-algebra-1-10 for $A=\begin{bmatrix} 0 & i\\ -i& 0 \end{bmatrix}$ how is (B) valid ?
o
asked
in
Linear Algebra
Jan 31
by
o
182
views
test-series
gateoverflow
linear-algebra
engineering-mathematics
22
votes
4
answers
13
GATE CSE 2015 Set 1 | Question: 36
Consider the following $2 \times 2$ matrix $A$ where two elements are unknown and are marked by $a$ and $b$. The eigenvalues of this matrix are $-1$ and $7.$ What are the values of $a$ and $b$? $\qquad A = \begin{pmatrix}1 & 4\\ b&a \end{pmatrix}$ $a = 6, b = 4$ $a = 4, b = 6$ $a = 3, b = 5$ $a = 5, b = 3 $
ProtonicRED
answered
in
Linear Algebra
Jan 17
by
ProtonicRED
4.8k
views
gatecse-2015-set1
linear-algebra
eigen-value
normal
0
votes
1
answer
14
linear algebra - eigenvalues
What are the eigenvalues of the following matrix?
Kabir5454
answered
in
Linear Algebra
Jan 14
by
Kabir5454
164
views
linear-algebra
eigen-value
matrix
engineering-mathematics
0
votes
0
answers
15
made easy test series - linear algebra
If 2 and -4 are the eigenvalues of a non-singular matrix A and |A| = -8, then the eigenvalues of adj(A) are x and -y. What is the value of x+y?
atulcse
asked
in
Linear Algebra
Jan 13
by
atulcse
169
views
linear-algebra
engineering-mathematics
made-easy-test-series
eigen-value
37
votes
8
answers
16
GATE CSE 2016 Set 1 | Question: 05
Two eigenvalues of a $3 \times 3$ real matrix $P$ are $(2+\sqrt {-1})$ and $3$. The determinant of $P$ is _______
ProtonicRED
answered
in
Linear Algebra
Jan 7
by
ProtonicRED
9.8k
views
gatecse-2016-set1
linear-algebra
eigen-value
numerical-answers
normal
3
votes
1
answer
17
#self doubt
How to solve this question?
Aditya_
answered
in
Linear Algebra
Dec 28, 2021
by
Aditya_
207
views
linear-algebra
eigen-value
0
votes
1
answer
18
Testbook Test Series
AngshukN
answered
in
Linear Algebra
Dec 22, 2021
by
AngshukN
117
views
testbook-test-series
0
votes
1
answer
19
Testbook Test Series
AngshukN
answered
in
Linear Algebra
Dec 22, 2021
by
AngshukN
134
views
testbook-test-series
3
votes
4
answers
20
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___
Isha_99
answered
in
Linear Algebra
Dec 17, 2021
by
Isha_99
320
views
test-series
engineering-mathematics
linear-algebra
system-of-equations
3
votes
1
answer
21
Applied Test Series
What is the value of the determinant ?
Isha_99
answered
in
Linear Algebra
Dec 17, 2021
by
Isha_99
210
views
test-series
engineering-mathematics
determinant
1
vote
0
answers
22
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
112
views
engineering-mathematics
eigen-value
linear-algebra
matrix
0
votes
0
answers
23
Testbook Test Series
rsansiya111
asked
in
Linear Algebra
Dec 11, 2021
by
rsansiya111
66
views
testbook-test-series
0
votes
0
answers
24
Testbook Test Series
rsansiya111
asked
in
Linear Algebra
Dec 11, 2021
by
rsansiya111
77
views
testbook-test-series
0
votes
0
answers
25
Testbook Test Series
rsansiya111
asked
in
Linear Algebra
Dec 11, 2021
by
rsansiya111
72
views
testbook-test-series
0
votes
0
answers
26
Testbook Test Series
rsansiya111
asked
in
Linear Algebra
Dec 11, 2021
by
rsansiya111
47
views
testbook-test-series
0
votes
0
answers
27
Testbook Test Series
rsansiya111
asked
in
Linear Algebra
Dec 11, 2021
by
rsansiya111
71
views
testbook-test-series
0
votes
0
answers
28
Testbook Test Series
rsansiya111
asked
in
Linear Algebra
Dec 11, 2021
by
rsansiya111
118
views
testbook-test-series
0
votes
0
answers
29
Testbook Test Series
rsansiya111
asked
in
Linear Algebra
Dec 11, 2021
by
rsansiya111
64
views
testbook-test-series
0
votes
0
answers
30
Testbook Test Series
rsansiya111
asked
in
Linear Algebra
Dec 11, 2021
by
rsansiya111
110
views
testbook-test-series
0
votes
1
answer
31
CMI-2021-Data Science
jugnu1337
answered
in
Linear Algebra
Dec 9, 2021
by
jugnu1337
118
views
linear-algebra
1
vote
0
answers
32
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
143
views
linear-algebra
0
votes
0
answers
33
NPTEL Assignment Question
rsansiya111
asked
in
Linear Algebra
Dec 8, 2021
by
rsansiya111
57
views
nptel-quiz
30
votes
4
answers
34
GATE CSE 2004 | Question: 27
Let $A, B, C, D$ be $n \times n$ matrices, each with non-zero determinant. If $ABCD = I$, then $B^{-1}$ is $D^{-1}C^{-1}A^{-1}$ $CDA$ $ADC$ Does not necessarily exist
Venky8
answered
in
Linear Algebra
Dec 8, 2021
by
Venky8
6.8k
views
gatecse-2004
linear-algebra
normal
matrix
0
votes
0
answers
35
NIELIT STA 2021
Let X be uniform random variable on [0,4] and Y be uniform random variable on [0,1]. If X and Y are independent, then P(max [X,Y] > 3) is equal to: 1 / 4 1 / 2 1 / 8 1
rsansiya111
asked
in
Linear Algebra
Dec 6, 2021
by
rsansiya111
85
views
engineering-mathematics
0
votes
0
answers
36
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
134
views
linear-algebra
0
votes
0
answers
37
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
161
views
linear-algebra
1
vote
3
answers
38
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 $a\cos \theta \neq b\sin \theta$
Amit_k_Singh
answered
in
Linear Algebra
Nov 5, 2021
by
Amit_k_Singh
419
views
nielit2016mar-scientistc
linear-algebra
matrix
2
votes
1
answer
39
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
2.2k
views
linear-algebra
engineering-mathematics
eigen-value
matrix
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Recent questions and answers in Linear Algebra
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