Recent questions tagged linear-algebra

+1 vote

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1

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) | 10 views

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0 answers

2

Gilbert Strang - Real Symmetric Matrices

asked Jun 2 in Linear Algebra by ankitgupta.1729 Loyal (6k points) | 34 views

0 votes

1 answer

3

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 (437 points) | 46 views

0 votes

2 answers

4

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 Junior (933 points) | 69 views

+1 vote

1 answer

5

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 (86.8k points) | 68 views

0 votes

1 answer

6

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 (71 points) | 44 views

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1 answer

7

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 Junior (933 points) | 55 views

+1 vote

3 answers

8

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 (86.8k points) | 163 views

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0 answers

9

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 (86.8k points) | 148 views

0 votes

1 answer

10

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 (113 points) | 76 views

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2 answers

11

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 (1.3k points) | 85 views

+1 vote

1 answer

12

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 (56.6k points) | 353 views

+1 vote

1 answer

13

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 (86.8k points) | 85 views

0 votes

1 answer

14

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 (495 points) | 92 views

0 votes

1 answer

15

GATE 2018 Maths - 22(Electronics and Communication Engineering)

asked Feb 21 in Calculus by Lakshman Patel RJIT Loyal (7.7k points) | 188 views

0 votes

1 answer

16

GATE 2018 Maths - 44(Electrical Engineering)

asked Feb 21 in Linear Algebra by Lakshman Patel RJIT Loyal (7.7k points) | 186 views

+10 votes

3 answers

17

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 (18k points) | 1.8k views

+6 votes

4 answers

18

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 (18k points) | 1.3k views

0 votes

0 answers

19

Eigen Vectors
I'm getting 2

asked Feb 1 in Linear Algebra by Pawan Kumar 2 Active (4.5k points) | 87 views

+5 votes

2 answers

20

LU decomposition

asked Jan 13 in Linear Algebra by Lakshman Patel RJIT Loyal (7.7k points) | 80 views

+5 votes

1 answer

21

Eigen value

asked Jan 13 in Linear Algebra by Lakshman Patel RJIT Loyal (7.7k points) | 123 views

+5 votes

1 answer

22

matrix linearly independent and orthogonal

asked Jan 12 in Linear Algebra by Lakshman Patel RJIT Loyal (7.7k points) | 65 views

+1 vote

0 answers

23

Linear Algebra
If $I$ is the unit matrix of order $n$ , where $k!=0$ is a constant then $adj \ kI$ is

asked Jan 11 in Linear Algebra by Anjan Active (1.7k points) | 77 views

+4 votes

1 answer

24

matrix adjoint

asked Jan 10 in Linear Algebra by Lakshman Patel RJIT Loyal (7.7k points) | 111 views

+3 votes

1 answer

25

matrix

asked Jan 10 in Linear Algebra by Lakshman Patel RJIT Loyal (7.7k points) | 58 views

+2 votes

0 answers

26

Matrix
If A and B are symmetric matrices of same order, then AB-BA is A) NULL matrix B) Symmetric matrix C) Skew symmetric matrix D) Orthogonal matrix

asked Jan 6 in Linear Algebra by srestha Veteran (86.8k points) | 116 views

+2 votes

0 answers

27

made easy subject wise
A real n × n matrix A = {aij} is defined as follows: aij= i, if i = j, otherwise 0 The determinant of all n eigen values of A is

asked Jan 6 in Mathematical Logic by Kuldeep Pal Active (1.3k points) | 50 views

+1 vote

1 answer

28

GATE 2014 IN (2 Marks)
A scalar valued function is defined as $f(x)=x^TAx+b^Tx+c$ , where A is a symmetric positive definite matrix with dimension $n*1$ ; b and x are vectors of dimension $n*1$ .The minimum value of $f(x)$ will occur when x equals. Answer: $-(\frac{A^{-1}b}{2})$ How to solve this?

asked Jan 2 in Linear Algebra by Sourajit25 Junior (791 points) | 126 views

+1 vote

1 answer

29

Linear Algebra: Matrix operations
Consider two statements:- 1) Eigenvalue of M = Eigenvalue of M' {M' is the matrix gets after row operation} 2) Eigenvalue of |M- $\lambda$I| = Eigenvalue of |M- $\lambda$I|' {|M- $\lambda$I|' is the matrix gets after row operation}

asked Jan 1 in Linear Algebra by Shubhanshu Boss (15k points) | 93 views

+2 votes

0 answers

30

Matrix, IN Gate 2007
Let A be an nxn real matrix such that A^2=I and y be an n-dimensional vector. Then the linear system of equations AX=Y has A) No solution B) Unique Solution C) More than one but finitely many independent solutions D) infinitely many independent solutions

asked Dec 31, 2017 in Linear Algebra by MiNiPanda Loyal (5.8k points) | 74 views

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