Recent questions and answers in Linear Algebra

+11 votes

6 answers

1

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 1 day ago in Linear Algebra by Prince Sindhiya Junior (707 points) | 981 views

+13 votes

4 answers

2

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 5 days ago in Linear Algebra by janeb abhishek (291 points) | 2.1k views

+20 votes

4 answers

3

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 5 days ago in Linear Algebra by janeb abhishek (291 points) | 1.3k views

+1 vote

2 answers

4

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 Junior (803 points) | 87 views

+1 vote

0 answers

5

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.

asked Jun 13 in Linear Algebra by pbhati (35 points) | 11 views

0 votes

0 answers

6

Matrix multiplication- Gilbert strang
Multiple Interpretations of Matrix Multiplications Say we are multiplying two matices A B = C. Multiple ways to interpret this operation: Row-wise approach: Ci = Ai B. Rows of C are linear combinations of rows in B Column multiplied by rows: ... of A and ith row of B! I am unable to understand these two ways as mentioned in gibert strang book and video ?

asked Jun 2 in Linear Algebra by Sandy Sharma (437 points) | 36 views

0 votes

0 answers

7

Gilbert Strang - Real Symmetric Matrices

asked Jun 2 in Linear Algebra by ankitgupta.1729 Loyal (6.1k points) | 34 views

+3 votes

3 answers

8

ISRO-DEC2017-1
Suppose $A$ is a finite set with $n$ elements.The number of elements and the rank of the largest equivalence relation on $A$ are $\{n,1\}$ $\{n,n\}$ $\{n^2,1\}$ $\{1,n^2\}$

answered May 31 in Linear Algebra by Sahreen (23 points) | 2.3k views

0 votes

2 answers

9

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 May 31 in Linear Algebra by srestha Veteran (86.9k points) | 70 views

0 votes

1 answer

10

Made easy test
Which of the following matrices is LU DECOMPOSIBLE? How to find it? $\begin{bmatrix} 1 & 2 & 3 \\ 2 & 4 & 5 \\ 1 & 3 & 4 \end{bmatrix}$ $\begin{bmatrix} 3 & 2 \\ 0 & 1 \end{bmatrix}$ $\begin{bmatrix} 0 & 1 \\ 3 & 2 \end{bmatrix}$ $\begin{bmatrix} 1 & -3 & 7 \\ -2 & 6 & 1 \\ 0 & 3 & -2 \end{bmatrix}$

answered May 31 in Linear Algebra by Kushagra Chatterjee Loyal (8.2k points) | 56 views

+1 vote

1 answer

11

Matrix
Each row of M can be represented as a linear combination of the other rows 1)Does that mean linear combination of other rows will be 0? how ? 2)And also , is linear combination means add, subtract, multiply and divide , but not squaring or root or exponential operation,right? https://gateoverflow.in/3319/gate2008-it-29

answered May 31 in Linear Algebra by Kushagra Chatterjee Loyal (8.2k points) | 68 views

0 votes

1 answer

12

If A and B are matrices of order 4 x 4 such that A= 5B and determinant of A = X. (determinant of B), then X will be

answered May 30 in Linear Algebra by Prateek Raghuvanshi Active (3.9k points) | 45 views

+27 votes

3 answers

13

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 May 29 in Linear Algebra by Prateek Raghuvanshi Active (3.9k points) | 3.4k views

+1 vote

3 answers

14

Matrix
The matrix $A=\begin{bmatrix} 1 &4 \\ 2 &3 \end{bmatrix}$ satisfies the following polynomial $A^{5}-4A^{4}-7A^{3}+11A^{2}-2A+kI=0$ Then the value of k is ______________

answered May 27 in Linear Algebra by Subarna Das Boss (10.7k points) | 165 views

0 votes

0 answers

15

asked May 20 in Linear Algebra by mehul vaidya Junior (993 points) | 34 views

0 votes

2 answers

16

ISRO-DEC2017-10
If vectors $\vec{a}=2\hat{i}+\lambda \hat{j}+\hat{k}$ and $\vec{b}=\hat{i}-2\hat{j}+3\hat{k}$ are perpendicular to each other, then value of $\lambda$ is $\dfrac{2}{5}$ $2$ $3$ $\dfrac{5}{2}$

answered May 19 in Linear Algebra by Mk Utkarsh Boss (12.6k points) | 726 views

0 votes

0 answers

17

Vector
https://www.youtube.com/watch?v=3SkCNpFOshk In this lecture , can somebody define in 2nd question why $X_{1}+X_{2}\notin V_{1}\cup V_{2}$? I cannot understand the proof

asked May 17 in Linear Algebra by srestha Veteran (86.9k points) | 26 views

0 votes

1 answer

18

ISI 2018 MMA 2
The volume of the region $S=\{(x,y,z) :\left | x \right |+\left | y \right |+\left | z \right |\leq 1\}$ is $\frac{1}{6}$ $\frac{1}{3}$ $\frac{2}{3}$ $\frac{4}{3}$

answered May 14 in Linear Algebra by Kushagra Chatterjee Loyal (8.2k points) | 69 views

+18 votes

5 answers

19

GATE2014-2-4
If the matrix $A$ is such that $$A= \begin{bmatrix} 2\\ −4\\7\end{bmatrix}\begin{bmatrix}1& 9& 5\end{bmatrix}$$ then the determinant of $A$ is equal to ______.

answered May 14 in Linear Algebra by srestha Veteran (86.9k points) | 1.3k views

0 votes

0 answers

20

Matrix
To find the product of the non-zero eigenvalues of the matrix is ____ $\begin{pmatrix} 1 & 0 & 0 & 0 & 1 \\ 0 & 1 & 1 & 1 & 0 \\ 0 & 1 & 1 & 1 & 0 \\ 0 & 1 & 1 & 1 & 0 \\ 1 & 0 & 0 ... [ \left ( 1-\lambda \right )\left ( \lambda ^{2}-2\lambda \right ) \right ]$ then $\lambda =-1,2,0$ Where is my mistake, plz tell me

asked May 14 in Linear Algebra by srestha Veteran (86.9k points) | 148 views

+1 vote

1 answer

21

Identify Lattice
Which of these diagrams are lattice and why?

answered May 7 in Linear Algebra by Deepakk Poonia (Dee) Boss (13.2k points) | 107 views

+2 votes

1 answer

22

Lattice
Lattice or not and why?

answered May 7 in Linear Algebra by Deepakk Poonia (Dee) Boss (13.2k points) | 115 views

+21 votes

3 answers

23

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 May 6 in Linear Algebra by srestha Veteran (86.9k points) | 3.2k views

+10 votes

3 answers

24

GATE2018-26
Consider a matrix P whose only eigenvectors are the multiples of $\begin{bmatrix} 1 \\ 4 \end{bmatrix}$. Consider the following statements. P does not have an inverse P has a repeated eigenvalue P cannot be diagonalized Which one of the following options ... and III are necessarily true Only II is necessarily true Only I and II are necessarily true Only II and III are necessarily true

answered May 6 in Linear Algebra by Ayush Upadhyaya Loyal (9k points) | 1.8k views

0 votes

2 answers

25

GATE 2016 EE SET 1
Let the eigenvalues of 2 x 2 matrix A be 1, -2 with eigenvectors x1 and x2 respectively. Then the eigenvalues and eigenvectors of the matrix A^2 - 3A+4I would respectively, be (a) 2,14; x1,x2 (b) 2,14; x1+x2:x1-x2 (c) 2,0; x1, x2 (d) 2,0; x1+x2,x1-x2

answered May 2 in Linear Algebra by Kushagra Chatterjee Loyal (8.2k points) | 85 views

+18 votes

2 answers

26

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 Apr 29 in Linear Algebra by mehul vaidya Junior (993 points) | 1.1k views

0 votes

3 answers

27

gilbert strang Problem Set 2.1
Which of the following descriptions are correct? The solutions x of Ax = $\begin{bmatrix} 1 & 1 & 1\\ 1 & 0 & 2 \end{bmatrix}$ $\begin{bmatrix} x1\\ x2\\ x3 \end{bmatrix}$ = $\begin{bmatrix} 0\\ 0\\ \end{bmatrix}$ form (a) a plane. (b) a line. (c) a point. (d) a subspace. (e) the nullspace of A. (f) the column space of A

answered Apr 27 in Linear Algebra by srestha Veteran (86.9k points) | 144 views

+1 vote

1 answer

28

EE,2016
Consider a $3\times 3$ matrix with every element being equal to 1 , its only non-zero eigenvalue is ....? $3\times 3 \begin{bmatrix} 1 & 1 &1 \\ 1 &1 &1 \\ 1 &1 &1 \end{bmatrix}$ now i solve in simple way ..directly $\left | A-\ ... \\ 0& 0 &0 \\ 0 & 0 &0 \end{bmatrix}$ but i got different eigen values why this happened ... i missed something ??

answered Apr 25 in Linear Algebra by AsiaPacific (43 points) | 414 views

0 votes

0 answers

29

ISI 2017 MMA 18
Consider following system of equations: $\begin{bmatrix} 1 &2 &3 &4 \\ 5&6 &7 &8 \\ a&9 &b &10 \\ 6&8 &10 & 13 \end{bmatrix}$$\begin{bmatrix} x1\\ x2\\ x3\\ x4 \end{bmatrix}$=$\begin{bmatrix} 0\\ 0\\ 0\\ 0 \end{bmatrix ... solution for ($x_{1},x_{2},x_{3},x_{4}$) is A) a parabola B) a straight line C) entire $\mathbb{R}^{2}$ D) a point

asked Apr 25 in Linear Algebra by Tesla! Boss (16.1k points) | 123 views

0 votes

1 answer

30

ISI 2017 MMA 16
Let ($x_{n}$) be a sequence of a real number such that the subsequence ($x_{2n}$) and ($x_{3n}$) converge to limit K and L respectively. Then A) ($x_{n}$) always converge B) If K=L then ($x_{n}$) converge C) ($x_{n}$) may not converge but K=L D) it is possible to have K$\neq$L

answered Apr 25 in Linear Algebra by Kushagra Chatterjee Loyal (8.2k points) | 104 views

0 votes

1 answer

31

ISI 2017 MMA 20
The number of the ordered pair (X, Y), where X and Y are N*N real matrices such that XY-YX= I is A) 0 B) 1 C) N D) Infinite

answered Apr 24 in Linear Algebra by Kushagra Chatterjee Loyal (8.2k points) | 114 views

+2 votes

4 answers

32

ISI-2017-29
Suppose the rank of the matrix $$\begin{pmatrix}1&1&2&2\\1&1&1&3\\a&b&b&1\end{pmatrix}$$ is $2$ for some real numbers $a$ and $b$. Then $b$ equals $1$ $3$ $1/2$ $1/3$

answered Apr 24 in Linear Algebra by Tesla! Boss (16.1k points) | 150 views

0 votes

1 answer

33

PGEE 2018
let $\left | A \right|=8$ ,$\left | B \right|=3$ ,$\left | C \right|=6$ then what will be value of AB$^{T}$C$^{-1}$ A) 144 B) 0 C) 4 D) 14

answered Apr 22 in Linear Algebra by Akhilesh Singla Active (4.7k points) | 199 views

0 votes

1 answer

34

PGEE 2018
let A and B be two n*n matrices such that they follow commutative property under multiplication operation which of the following follows commutative property 1) $A^{T} B$ 2) $B^{T} A$ 3) $A^{T} B^{T}$ 4) None

answered Apr 21 in Linear Algebra by Sayan Bose Active (2.3k points) | 99 views

0 votes

2 answers

35

ISRO 2013- Polynomials [EE]
The unique polynomial P(x) of degree 2 such that: P(1) = 1, P(3) = 27, P(4) = 64 is a) 8x2 -19x + 12 b) 8x2 + 19x + 12 c) -8x2 -19x + 12 d) -8x2 -19x - 12

answered Apr 20 in Linear Algebra by sampurnanand mishra (123 points) | 220 views

0 votes

1 answer

36

Self doubt
There are 10 different balls in such way that 6 balls are white and 4 balls are black. How many different arrangements are possible such way that black ball placed before the white ball ?

answered Apr 19 in Linear Algebra by Subarna Das Boss (10.7k points) | 46 views

+1 vote

2 answers

37

linear algebra

answered Apr 16 in Linear Algebra by pankaj_vir Loyal (8.5k points) | 51 views

+9 votes

3 answers

38

GATE2004-IT-6
What values of x, y and z satisfy the following system of linear equations? $$\begin{bmatrix} 1 &2 &3 \\ 1& 3 &4 \\ 2& 2 &3 \end{bmatrix} \begin{bmatrix} x\\y \\ z \end{bmatrix} = \begin{bmatrix} 6\\8 \\ 12 \end{bmatrix}$$ $x = 6$, $y = 3$, $z = 2$ $x = 12$, $y = 3$, $z = - 4$ $x = 6$, $y = 6$, $z = - 4$ $x = 12$, $y = - 3$, $z = 0$

answered Apr 12 in Linear Algebra by Ayush Upadhyaya Loyal (9k points) | 727 views

+8 votes

2 answers

39

GATE2002-1.1
The rank of the matrix $\begin{bmatrix} 1 & 1 \\ 0 & 0 \end{bmatrix}$ is $4$ $2$ $1$ $0$

answered Apr 6 in Linear Algebra by Sayed Athar (93 points) | 567 views

0 votes

1 answer

40

Gate 2004 Question on Linear Algebra
Can Somebody Please explain me in detail description how to calculate the number of upper triangular and lower triangular of a square matrix I read somewhere that it turns out to be ((n^2)+n) /2,Can someone please provide me with a proof

answered Apr 2 in Linear Algebra by gari Active (3.2k points) | 75 views

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