Recent questions tagged linear-algebra

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1

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

asked 1 day ago in Linear Algebra by suparna kar (49 points) | 14 views

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0 answers

2

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

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2 answers

3

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 $A^{-1}$.

asked Aug 8 in Linear Algebra by pankaj_vir Loyal (9.2k points) | 49 views

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1 answer

4

Discrete maths approach
Can you please guide me how to approach discrete maths? I want prepare it alongside with what's being taught at classroom coaching, please suggest resources and strategy

asked Jul 30 in Set Theory & Algebra by Ajaaz (17 points) | 35 views

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1 answer

5

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.

asked Jul 5 in Linear Algebra by ZeroFriction (15 points) | 68 views

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1 answer

6

linear algebra
the product of the non-zero eigen values of the matrax 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 how can we solve this question?

asked Jul 2 in Mathematical Logic by suneetha (97 points) | 16 views

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3 answers

7

linear algebra
Let A be the 2 × 2 matrix with elements a11 = a12 = a21 = +1 and a22 = −1. Then the eigenvalues of the matrix A19 are (a) 1024 and−1024 (b) 1024√2 and −1024√2 (c) 4√2 and−4√2 (d) 512√2 and−512√2

asked Jul 2 in Mathematical Logic by suneetha (97 points) | 32 views

+1 vote

0 answers

8

Kenneth Rosen
where would i get solution or answers for exercise problem of discrete mathematics by Kenneth rosen and linear algebra by Gilbert strang?

asked Jun 27 in Mathematical Logic by Rishav Kumar Singh Active (2.3k points) | 39 views

+1 vote

1 answer

9

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) | 29 views

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0 answers

10

Gilbert Strang - Real Symmetric Matrices

asked Jun 2 in Linear Algebra by ankitgupta.1729 Loyal (6.6k points) | 40 views

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1 answer

11

Gilbert Strang 1.3.9
For which three numbers $k$ does elimination break down? Which is fixed by a row exchange? In each case, is the number of solutions $0$ or $1$ Infinity? $$Kx + 3 y =6\\3x +ky = -6$$

asked May 31 in Engineering Mathematics by Sandy Sharma Junior (677 points) | 56 views

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3 answers

12

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.

asked May 31 in Linear Algebra by saumya mishra Active (1.2k points) | 108 views

+1 vote

1 answer

13

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

asked May 30 in Linear Algebra by srestha Veteran (92k points) | 88 views

0 votes

1 answer

14

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

asked May 30 in Linear Algebra by VIDYADHAR SHELKE 1 (111 points) | 59 views

0 votes

1 answer

15

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

asked May 30 in Linear Algebra by saumya mishra Active (1.2k points) | 64 views

+1 vote

3 answers

16

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 ______________

asked May 26 in Linear Algebra by srestha Veteran (92k points) | 206 views

0 votes

0 answers

17

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 (92k points) | 159 views

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1 answer

18

Regarding Preparation
I know this question has been asked many times, but yeah. I am weak in calculus and linear algebra and have never studied probability properly. Now according to internet suggestions, I should read Kreyzig or BS Grewal, but I will most probably want ... time for GATE 2019 should i watch lectures of Gilbert Strang, Stats 110 and calculus textbook, or should i stick to kreyzig?

asked May 11 in Calculus by mohitjarvissharma (351 points) | 83 views

0 votes

2 answers

19

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

asked May 2 in Linear Algebra by Prateek K Active (1.4k points) | 106 views

+1 vote

1 answer

20

Set system and linear algebra
We have $m$ sets $A_1,A_2,A_3 \text{ to } A_m$. All $A_i \subseteq [n]$ where $ [n] = \{1,2,3, \dots n \}.$ Given that $|A_i| = \text{odd number}$ and $|A_i \cap A_j| = \text{even number }\forall i \neq j$. Show that $m \leq n$.

asked Apr 16 in Set Theory & Algebra by Debashish Deka Veteran (56.9k points) | 376 views

+1 vote

1 answer

21

Determinant
Find the determinant of the $n\times n$ matrix $\begin{bmatrix} 2cos\Theta & 1 & 0 &0 &........ & 0 & \\ 1&2cos\Theta &1 & 0 & ........ & 0 & \\ 0&1 & 2cos\Theta & 1 &........ & 0 & ... &.... & 1 & 2cos\Theta & \end{bmatrix}$ how the answer could be $D_{n}-2cos\Theta D_{n-1}+D_{n-2}=0$? Plz explain

asked Mar 13 in Linear Algebra by srestha Veteran (92k points) | 96 views

0 votes

1 answer

22

GATE-2007 EE
Let $x$ and $y$ be two vectors in a $3$ dimensional space and $<x,y>$ denote their dot product. Then the determinant $det\begin{bmatrix}<x,x> & <x,y>\\ <y,x> & <y,y>\end{bmatrix}$ is zero when $x$ and $y$ are ... positive when $x$ and $y$ are linearly independent is non-zero for all non-zero $x$ and $y$ is zero only when either $x$ or $y$ is zero

asked Mar 13 in Linear Algebra by Aishwarya Gujrathi Junior (503 points) | 103 views

0 votes

1 answer

23

GATE 2018 Maths - 22(Electronics and Communication Engineering)

asked Feb 21 in Calculus by Lakshman Patel RJIT Loyal (8k points) | 211 views

0 votes

2 answers

24

GATE 2018 Maths - 44(Electrical Engineering)

asked Feb 21 in Linear Algebra by Lakshman Patel RJIT Loyal (8k points) | 208 views

+10 votes

3 answers

25

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

asked Feb 14 in Linear Algebra by gatecse Boss (18.1k points) | 2.1k views

+6 votes

4 answers

26

GATE2018-17
Consider a matrix $A= uv^T$ where $u=\begin{pmatrix}1 \\ 2 \end{pmatrix} , v = \begin{pmatrix}1 \\1 \end{pmatrix}$. Note that $v^T$ denotes the transpose of $v$. The largest eigenvalue of $A$ is ____

asked Feb 14 in Linear Algebra by gatecse Boss (18.1k points) | 1.4k views

0 votes

0 answers

27

Eigen Vectors
I'm getting 2

asked Feb 1 in Linear Algebra by Pawan Kumar 2 Active (4.5k points) | 91 views

+5 votes

2 answers

28

LU decomposition

asked Jan 13 in Linear Algebra by Lakshman Patel RJIT Loyal (8k points) | 84 views

+5 votes

1 answer

29

Eigen value

asked Jan 13 in Linear Algebra by Lakshman Patel RJIT Loyal (8k points) | 130 views

+5 votes

1 answer

30

matrix linearly independent and orthogonal

asked Jan 12 in Linear Algebra by Lakshman Patel RJIT Loyal (8k points) | 71 views

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