Recent questions and answers in Linear Algebra

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0 answers

1

B-tech
Symmetrical question

asked 1 day ago in Linear Algebra by S. Sindhu (7 points) | 9 views

0 votes

1 answer

2

Gate 2015 CE set 2
The two eigen values of the matrix $\begin{bmatrix} 2 & 1\\ 1& p \end{bmatrix}$ have a ratio of 3:1 for p= 2. What is another value of p for which eigenvalues have the same ratio of 3:1? A)-2 b) 1 c) 7/3 d)14/3

answered 3 days ago in Linear Algebra by MiNiPanda Loyal (8.9k points) | 14 views

0 votes

0 answers

3

Eigen vector
Is it true that if we have 3 distinct eigen vectors x,y and z than x,y and z would respectively be orthogonal to each other .Please elaborate

asked 3 days ago in Linear Algebra by Shivangi Parashar 2 (41 points) | 15 views

0 votes

1 answer

4

Gate 2016 ME Set 2
The condition for which the eigen values of the matrix A = $\begin{pmatrix} 2 &1 \\ 1& k \end{pmatrix}$ are positive, is a) k>1/2 b) k>-2 c) k>0 d) k< -1/2

answered 3 days ago in Linear Algebra by Prince Sindhiya Active (2.3k points) | 15 views

0 votes

1 answer

5

Gate 2016 CE Set 1
If the entries in each column of a square matrix M add up to 1, then an eigen value of M is A) 4 B) 3 C) 2 D) 1

answered 3 days ago in Linear Algebra by Shivani gaikawad (371 points) | 33 views

0 votes

1 answer

6

made easy ME previou year question
which on of the following is an eigenvector of the matrix [5 0 0 0 0 5 5 0 0 0 2 1 0 0 3 1] a) [1 -2 0 0 ]t b) [0 0 1 0]t c) [1 0 0 -2]t d) [1 -1 2 1]t

answered 3 days ago in Linear Algebra by Prince Sindhiya Active (2.3k points) | 17 views

0 votes

0 answers

7

Gate-2016
A 3×3 matrix p is such that,p^3=p. Then eigen values of p are

asked 5 days ago in Linear Algebra by lg (33 points) | 15 views

+17 votes

3 answers

8

GATE2015-3-33
If the following system has non-trivial solution, $px + qy + rz = 0$ $qx + ry + pz = 0$ $rx + py + qz = 0$, then which one of the following options is TRUE? $p - q + r = 0 \text{ or } p = q = -r$ $p + q - r = 0 \text{ or } p = -q = r$ $p + q + r = 0 \text{ or } p = q = r$ $p - q + r = 0 \text{ or } p = -q = -r$

answered Aug 13 in Linear Algebra by aditi19 (261 points) | 1.9k views

0 votes

1 answer

9

gate 2014
Two matrices A and B are given below: A= p q r s B= p2 + q2 pr + qs pr +qs r2 + s2 If the rank of matrix A is N, then the rank of matrix B is (A) N /2 (B) N-1 (C) N (D) 2 N

answered Aug 10 in Linear Algebra by arvin Active (3.6k points) | 26 views

+1 vote

2 answers

10

Engineering mathematics
if the sum of the diagonal elements of a 2x2 matrix is (-6) then the maximum possible value of determinant of the matrix is

answered Aug 9 in Linear Algebra by Deepanshu Junior (743 points) | 48 views

0 votes

2 answers

11

Engineering Mathematics - Linear Algebra

answered Aug 9 in Linear Algebra by arvin Active (3.6k points) | 170 views

0 votes

0 answers

12

Invertible Matrix
Let $A$ be a nilpotent matrix. Show that $I + A$ is invertible.

asked Aug 8 in Linear Algebra by pankaj_vir Loyal (9.2k points) | 11 views

0 votes

2 answers

13

Invertible Matrix
Let A be a $5 × 5$ invertible matrix with row sums $1$. That is $\sum_{j=1}^{5} a_{ij} = 1$ for $1 \leq i\leq 5$. Then, what is the sum of all entries of $A^{-1}$.

answered Aug 8 in Linear Algebra by Rishabh Gupta 2 Boss (14.4k points) | 49 views

+3 votes

1 answer

14

TIFR-2015-Maths-A-1
Let $A$ be an invertible $10 \times 10$ matrix with real entries such that the sum of each row is $1$. Then The sum of the entries of each row of the inverse of $A$ is $1$. The sum of the entries of each column of the inverse of $A$ is $1$. The trace of the inverse of $A$ is non-zero. None of the above.

answered Aug 8 in Linear Algebra by Rishabh Gupta 2 Boss (14.4k points) | 103 views

+6 votes

3 answers

15

GATE1987-1-xxi
If $a, b,$ and $c$ are constants, which of the following is a linear inequality? $ax+bcy=0$ $ax^{2}+cy^{2}=21$ $abx+a^{2}y \geq 15$ $xy+ax \geq 20$

answered Aug 8 in Linear Algebra by Nikhilesh AS (11 points) | 495 views

0 votes

1 answer

16

#idempotent #matrix
If Matrix A and B are of same size and AB=B and BA=A. Then the value of $(A+B)^{5}$ is _____________?

answered Aug 8 in Linear Algebra by arvin Active (3.6k points) | 30 views

+27 votes

4 answers

17

GATE2017-1-31
Let $A$ be $n\times n$ real valued square symmetric matrix of rank 2 with $\sum_{i=1}^{n}\sum_{j=1}^{n}A^{2}_{ij} =$ 50. Consider the following statements. One eigenvalue must be in $\left [ -5,5 \right ]$ The eigenvalue with the largest ... greater than 5 Which of the above statements about eigenvalues of $A$ is/are necessarily CORRECT? Both I and II I only II only Neither I nor II

answered Jul 20 in Linear Algebra by Gyanu (31 points) | 3.6k views

+7 votes

3 answers

18

ISI2016
Let $A$ be a matrix such that: $A=\begin{pmatrix} -1 & 2\\ 0 & -1 \end{pmatrix}$ and $B=A+A^2+A^3+\ldots +A^{50}$. Then which of the following is true? $B^{2}=I$ $B^{2}=0$ $B^{2}=B$ None of the above

answered Jul 16 in Linear Algebra by Ayush Upadhyaya Boss (11.1k points) | 395 views

+19 votes

3 answers

19

GATE1996-1.7
Let $Ax = b$ be a system of linear equations where $A$ is an $m \times n$ matrix and $b$ is a $m \times 1$ column vector and $X$ is an $n \times1$ column vector of unknowns. Which of the following is false? The system has a solution if and only if, both $A$ ... a unique solution. The system will have only a trivial solution when $m=n$, $b$ is the zero vector and $\text{rank}(A) =n$.

answered Jul 15 in Linear Algebra by Ayush Upadhyaya Boss (11.1k points) | 1.7k views

+16 votes

5 answers

20

GATE2014-1-4
Consider the following system of equations: $3x + 2y = 1 $ $4x + 7z = 1 $ $x + y + z = 3$ $x - 2y + 7z = 0$ The number of solutions for this system is ______________

answered Jul 15 in Linear Algebra by Ayush Upadhyaya Boss (11.1k points) | 2.1k views

+21 votes

4 answers

21

GATE2017-1-3
Let $c_{1}.....c_{n}$ be scalars, not all zero, such that $\sum_{i=1}^{n}c_{i}a_{i}$ = 0 where $a_{i}$ are column vectors in $R^{n}$. Consider the set of linear equations $Ax = b$ where $A=\left [ a_{1}.....a_{n} \ ... of equations has a unique solution at $x=J_{n}$ where $J_{n}$ denotes a $n$-dimensional vector of all 1. no solution infinitely many solutions finitely many solutions

answered Jul 15 in Linear Algebra by Ayush Upadhyaya Boss (11.1k points) | 3.3k views

+18 votes

3 answers

22

GATE2008-IT-29
If $M$ is a square matrix with a zero determinant, which of the following assertion (s) is (are) correct? S1: Each row of $M$ can be represented as a linear combination of the other rows S2: Each column of $M$ can be represented as a linear combination of the ... : $MX = 0$ has a nontrivial solution S4: $M$ has an inverse $S3$ and $S2$ $S1$ and $S4$ $S1$ and $S3$ $S1, S2$ and $S3$

answered Jul 15 in Linear Algebra by Ayush Upadhyaya Boss (11.1k points) | 1.2k views

+13 votes

2 answers

23

GATE1993-01.1
In questions $1.1$ to $1.7$ below, one or more of the alternatives are correct. Write the code letter$(s)$ $a$, $b$, $c$, $d$ corresponding to the correct alternative$(s) $ in the answer book. Marks will be given only if all the correct alternatives have been selected and no incorrect alternative is ... },\alpha \neq 0$$ is (are) $(0,0,\alpha)$ $(\alpha,0,0)$ $(0,0,1)$ $(0,\alpha,0)$

answered Jul 14 in Linear Algebra by Ayush Upadhyaya Boss (11.1k points) | 1.1k views

+32 votes

6 answers

24

GATE2014-2-47
The product of the non-zero eigenvalues of the matrix is ____ $\begin{pmatrix} 1 & 0 & 0 & 0 & 1 \\ 0 & 1 & 1 & 1 & 0 \\ 0 & 1 & 1 & 1 & 0 \\ 0 & 1 & 1 & 1 & 0 \\ 1 & 0 & 0 & 0 & 1 \end{pmatrix}$

answered Jul 14 in Linear Algebra by Ayush Upadhyaya Boss (11.1k points) | 6.2k views

0 votes

0 answers

25

Kenneth Rosen 2.1
Determine True or False $a)x\varepsilon \left \{ x \right \}$ $b)\left \{ x \right \}\subseteq \left \{ x \right \}$ $c)\left \{ x \right \}\varepsilon \left \{ x \right \}$

asked Jul 13 in Linear Algebra by srestha Veteran (92.2k points) | 37 views

+15 votes

5 answers

26

GATE2015-3-15
In the given matrix $\begin{bmatrix} 1 & -1 & 2 \\ 0 & 1 & 0 \\ 1 & 2 & 1 \end{bmatrix}$ , one of the eigenvalues is 1. The eigenvectors corresponding to the eigenvalue 1 are $\left\{a\left(4,2,1\right) \mid a \neq 0, a \in \mathbb{R}\right\}$ $\ ... \neq 0, a \in \mathbb{R}\right\}$ $\left\{a\left(- \sqrt{2},0,1\right) \mid a \neq 0, a \in \mathbb{R}\right\}$

answered Jul 13 in Linear Algebra by Ayush Upadhyaya Boss (11.1k points) | 1.7k views

+12 votes

2 answers

27

GATE 2013 EC-A-27
Let A be an mxn matrix and B an nxm matrix. It is given that determinant ( Im + AB ) = determinant ( In + BA ) , where Ik is the k×k identity matrix. Using the above property, the determinant of the matrix given below is $\begin{bmatrix} 2& 1& 1& 1\\ 1& 2& 1& 1\\ 1& 1& 2& 1\\ 1& 1& 1& 2 \end{bmatrix}$ A) 2 B) 5 C) 8 D) 16

answered Jul 13 in Linear Algebra by Ayush Upadhyaya Boss (11.1k points) | 661 views

0 votes

1 answer

28

ugc net 2018 july-10

answered Jul 9 in Linear Algebra by Sanjay Sharma Boss (48.8k points) | 139 views

0 votes

0 answers

29

orthogonal matrix
Is the determinent of both the orthogonal and orthonormal is +-1?for orthonormal im always getting +-1 but for orthogonal its always +-C,not 1,C=mag of the vector matrix

asked Jul 8 in Linear Algebra by Ankush Saha (7 points) | 25 views

0 votes

1 answer

30

Inversion of a matrix - CSIR question
Let A be 3x3 matrix. Suppose 1 and -1 are two of the three Eigen Values of A and 18 is one of the Eigen Values of A2+3A. Then____ a.) Both A and A2+3A are invertible. b.) A2+3A but A is not. c.) A is invertible but A2+3A is not invertible. d.) Both A and A2+3A are not invertible.

answered Jul 5 in Linear Algebra by abhishekmehta4u Boss (22.6k points) | 68 views

0 votes

3 answers

31

Made easy test
Consider the rank of matrix $'A'$ of size $(m \times n)$ is $"m-1"$. Then, which of the following is true? $AA^T$ will be invertible. $A$ have $"m-1"$ linearly independent rows and $"m-1"$ linearly ... and $"n"$ linearly independent columns. $A$ will have $"m-1"$ linearly independent rows and $"n-1"$ independent columns.

answered Jun 29 in Linear Algebra by Navneet Kalra (141 points) | 109 views

0 votes

2 answers

32

GATE 2018 Maths - 44(Electrical Engineering)

answered Jun 29 in Linear Algebra by Vinod Jaggavarapu (17 points) | 208 views

+1 vote

1 answer

33

Engineering Maths: Orthogonal Matrix
Is the given last point correct? But as i see in the given matrix sum of the product of first two columns (or) two rows is not zero. please verify.

answered Jun 29 in Linear Algebra by Vinod Jaggavarapu (17 points) | 29 views

+1 vote

4 answers

34

ISI-2016-04
If $a,b,c$ and $d$ satisfy the equations $$a+7b+3c+5d =16\\8a+4b+6c+2d = -16\\ 2a+6b+4c+8d = 16 \\ 5a+3b+7c+d= -16$$ Then $(a+d)(b+c)$ equals $-4$ $0$ $16$ $-16$

answered Jun 28 in Linear Algebra by Navneet Kalra (141 points) | 122 views

+1 vote

1 answer

35

Test Series ACE
How to solve? ________________ Number of non-negative integer solutions such that x+y+z=17 where x>1,y>2,z>3 is --------

answered Jun 28 in Linear Algebra by Navneet Kalra (141 points) | 82 views

+1 vote

1 answer

36

GATE Linear Algebra
For what values of $\lambda$ the system of equations will have $2$ linear independent solutions - $x + y + z = 0$ $(\lambda + 1) y + (\lambda + 1) z = 0$ ($\lambda^{2}- 1) z = 0$ Now the problem i'm facing is if there is ... rank of matrix will be $1$. Can anyone please explain in simple why the rank of matrix should be $1$ if we need $2$ Linear Independent solution. Thankyou.

answered Jun 28 in Linear Algebra by Navneet Kalra (141 points) | 84 views

+11 votes

6 answers

37

GATE2001-1.1
Consider the following statements: S1: The sum of two singular $n \times n$ matrices may be non-singular S2: The sum of two $n \times n$ non-singular matrices may be singular Which one of the following statements is correct? $S1$ and $S2$ both are true $S1$ is true, $S2$ is false $S1$ is false, $S2$ is true $S1$ and $S2$ both are false

answered Jun 23 in Linear Algebra by Prince Sindhiya Active (2.3k points) | 1k views

+14 votes

4 answers

38

GATE2004-26
The number of different $n \times n $ symmetric matrices with each element being either 0 or 1 is: (Note: $\text{power} \left(2, X\right)$ is same as $2^X$) $\text{power} \left(2, n\right)$ $\text{power} \left(2, n^2\right)$ $\text{power} \left(2,\frac{ \left(n^2+ n \right) }{2}\right)$ $\text{power} \left(2, \frac{\left(n^2 - n\right)}{2}\right)$

answered Jun 19 in Linear Algebra by janeb abhishek (357 points) | 2.3k views

+20 votes

4 answers

39

GATE2006-23
$F$ is an $n\times n$ real matrix. $b$ is an $n\times 1$ real vector. Suppose there are two $n\times 1$ vectors, $u$ and $v$ such that, $u ≠ v$ and $Fu = b, Fv = b$. Which one of the following statements is false? Determinant of $F$ is zero. There are an infinite number of solutions to $Fx = b$ There is an $x≠0$ such that $Fx = 0$ $F$ must have two identical rows

answered Jun 19 in Linear Algebra by janeb abhishek (357 points) | 1.3k views

+1 vote

2 answers

40

mathematics
Consider the set H of all 3 × 3 matrices of the type where a, b, c, d, e and f are real numbers and abc ≠ 0. Under the matrix multiplication operation, the set H is a group a monoid but not a group C a semigroup but not a monoid D neither a group nor a semigroup

answered Jun 13 in Linear Algebra by talha hashim Active (2.1k points) | 87 views

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