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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

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

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

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

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

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

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

1.2k views

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

7.1k views

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

6.9k views

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

1.0k views

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

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

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

4.8k views

0 votes

1 answer

14

linear algebra - eigenvalues
What are the eigenvalues of the following matrix?

Kabir5454 answered in Linear Algebra Jan 14

164 views

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

169 views

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

9.8k views

3 votes

1 answer

17

#self doubt
How to solve this question?

Aditya_ answered in Linear Algebra Dec 28, 2021

207 views

0 votes

1 answer

18

Testbook Test Series

AngshukN answered in Linear Algebra Dec 22, 2021

117 views

0 votes

1 answer

19

Testbook Test Series

AngshukN answered in Linear Algebra Dec 22, 2021

134 views

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

320 views

3 votes

1 answer

21

Applied Test Series
What is the value of the determinant ?

Isha_99 answered in Linear Algebra Dec 17, 2021

210 views

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

112 views

0 votes

0 answers

23

Testbook Test Series

rsansiya111 asked in Linear Algebra Dec 11, 2021

66 views

0 votes

0 answers

24

Testbook Test Series

rsansiya111 asked in Linear Algebra Dec 11, 2021

77 views

0 votes

0 answers

25

Testbook Test Series

rsansiya111 asked in Linear Algebra Dec 11, 2021

72 views

0 votes

0 answers

26

Testbook Test Series

rsansiya111 asked in Linear Algebra Dec 11, 2021

47 views

0 votes

0 answers

27

Testbook Test Series

rsansiya111 asked in Linear Algebra Dec 11, 2021

71 views

0 votes

0 answers

28

Testbook Test Series

rsansiya111 asked in Linear Algebra Dec 11, 2021

118 views

0 votes

0 answers

29

Testbook Test Series

rsansiya111 asked in Linear Algebra Dec 11, 2021

64 views

0 votes

0 answers

30

Testbook Test Series

rsansiya111 asked in Linear Algebra Dec 11, 2021

110 views

0 votes

1 answer

31

CMI-2021-Data Science

jugnu1337 answered in Linear Algebra Dec 9, 2021

118 views

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

143 views

0 votes

0 answers

33

NPTEL Assignment Question

rsansiya111 asked in Linear Algebra Dec 8, 2021

57 views

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

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

85 views

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

134 views

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

161 views

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

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

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Recent questions and answers in Linear Algebra