Recent questions tagged linear-algebra

Recent questions tagged linear-algebra

1 vote

1 answer

1

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” ?

samarpita asked in Linear Algebra May 9

37 views

1 vote

1 answer

2

Eigen Values of an orthogonal matrix will always be +1 and the modulus will also be always |1|?

samarpita asked in Linear Algebra May 9

77 views

2 votes

2 answers

3

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

by Arjun

748 views

3 votes

3 answers

4

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

by Arjun

755 views

1 vote

1 answer

5

GATE CSE 2022 | Question: 43
Which of the following is/are the eigenvector(s) for the matrix given below? $\begin{pmatrix} - 9 & - 6 & - 2 & - 4 \\ - 8 & - 6 & - 3 & - 1 \\ 20 & 15 & 8 & 5 \\ 32 & 21 & 7 & 12 \end{pmatrix}$ ... $\begin{pmatrix} - 1 \\ 0 \\ 2 \\ 2 \end{pmatrix}$ $\begin{pmatrix} 0 \\ 1 \\ - 3 \\ 0 \end{pmatrix}$

Arjun asked in Linear Algebra Feb 15

by Arjun

741 views

0 votes

0 answers

6

(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

140 views

0 votes

1 answer

7

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

atulcse asked in Linear Algebra Jan 13

119 views

0 votes

0 answers

8

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

125 views

3 votes

1 answer

9

#self doubt
How to solve this question?

samarpita asked in Linear Algebra Dec 28, 2021

167 views

1 vote

0 answers

10

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

89 views

0 votes

1 answer

11

CMI-2021-Data Science

rsansiya111 asked in Linear Algebra Dec 9, 2021

93 views

1 vote

0 answers

12

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

71 views

0 votes

0 answers

13

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

117 views

0 votes

0 answers

14

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

142 views

2 votes

0 answers

15

Applied Grand Test 2
What is the value of the given determinant ?

LRU asked in Linear Algebra Nov 22, 2021

by LRU

247 views

3 votes

4 answers

16

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

244 views

2 votes

1 answer

17

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

2.0k views

16 votes

6 answers

18

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

6.5k views

9 votes

2 answers

19

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

4.9k views

2 votes

1 answer

20

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

283 views

0 votes

3 answers

21

CMI-2018-DataScience-A: 2
Let ... $|A|=|B|$ $|C|=|D|$ $|B|=-|C|$ $|A|=-|D|$

soujanyareddy13 asked in Others Jan 29, 2021

by soujanyareddy13

298 views

2 votes

2 answers

22

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

238 views

1 vote

1 answer

23

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

261 views

0 votes

2 answers

24

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

165 views

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