Recent questions tagged linear-algebra

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1

GATE 2017 (EC) Eigen Value
For the given matrix $A$, one of the Eigenvalue is real $A=\begin{bmatrix} 1 &2 &3 &4 &5 \\ 5 &1 &2 &3 &4 \\ 4&5 &1 &2 &3 \\ 3&4 &5 &1 &2 \\ 2 &3 &4 &5 &1 \end{bmatrix}$ The real Eigen value is: $A)2.5$ $B)0$ $C)15$ $D)25$

asked 3 hours ago in Linear Algebra by Lakshman Patel RJIT Loyal (9.6k points) | 11 views

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2

number of linearly indendent eigen vectors

asked 4 days ago in Linear Algebra by MIRIYALA JEEVAN KUMA Active (2.2k points) | 21 views

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3

Linear Algebra
We know, the eigen value for upper triangular/lower triangular/diagonal matrices are the diagonal elements of the matrix. https://gateoverflow.in/858/gate2002-5a This question, https://gateoverflow.in/1174/gate2005-49 If apply row transformation to convert it ... make the given matrix to upper triangular matrix, so that eigen values will be equal to the elements in the diagonals?

asked Oct 5 in Linear Algebra by Swapnil Naik Active (1.3k points) | 31 views

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1 answer

4

GATE2016 37 Mathematics
Let $M = \begin{bmatrix} a & b &c \\ b &d & e\\ c & e & f \end{bmatrix}$ be a real matrix with eigenvalues 1, 0 and 3. If the eigenvectors corresponding to 1 and 0 are $\left ( 1,1,1 \right )^T$ and $\left ( 1,-1, 0 \right )^T$ respectively, then the value of 3f is equal to _______.

asked Oct 4 in Linear Algebra by Mk Utkarsh Boss (20.1k points) | 90 views

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5

Which books are good to practice linear algebra and calculas?

asked Oct 1 in GATE by aditi19 Junior (863 points) | 11 views

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1 answer

6

Linear Algebra RGPV 2001
Test the consistency of the following system of equations and solve if possible $3x + 3y +2z = 1$ $x + 2y = 4$ $10y + 3z = -2$ $2x - 3y -z = 5$

asked Sep 29 in Linear Algebra by Mk Utkarsh Boss (20.1k points) | 42 views

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7

Hk Dass Linear Algebra
Test the consistency of the following system of equations $5x + 3y + 7z = 4 $ $3x + 26y + 2z = 9$ $7x + 2y + 10z = 5$

asked Sep 29 in Linear Algebra by Mk Utkarsh Boss (20.1k points) | 25 views

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8

Linear system of equations

asked Sep 16 in Linear Algebra by Na462 Loyal (6.4k points) | 22 views

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1 answer

9

Engineering Maths
If A = $\begin{bmatrix} -1 & 1 & 0 \\ 0 & 2 &-2 \\ 0& 0 & 3 \end{bmatrix}$ then trace of the matrix 3A2 + adj A is ____

asked Aug 23 in Linear Algebra by suparna kar (87 points) | 33 views

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10

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 Aug 17 in Linear Algebra by suparna kar (87 points) | 36 views

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11

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

asked Aug 8 in Linear Algebra by pankaj_vir Loyal (9.6k points) | 32 views

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2 answers

12

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 (9.6k points) | 76 views

+1 vote

1 answer

13

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 (33 points) | 46 views

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1 answer

14

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) | 87 views

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15

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 (237 points) | 20 views

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3 answers

16

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 Linear Algebra by suneetha (237 points) | 39 views

+1 vote

1 answer

17

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) | 34 views

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18

Gilbert Strang - Real Symmetric Matrices

asked Jun 2 in Linear Algebra by ankitgupta.1729 Loyal (7.6k points) | 43 views

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19

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 (949 points) | 59 views

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3 answers

20

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 (1.4k points) | 124 views

+1 vote

1 answer

21

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 (98.4k points) | 103 views

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1 answer

22

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 (143 points) | 62 views

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1 answer

23

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 (1.4k points) | 69 views

+1 vote

3 answers

24

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 (98.4k points) | 223 views

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25

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 (98.4k points) | 173 views

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26

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 (357 points) | 87 views

+1 vote

2 answers

27

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 (1.5k points) | 125 views

+1 vote

1 answer

28

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 (57.4k points) | 385 views

+1 vote

1 answer

29

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 (98.4k points) | 101 views

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1 answer

30

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 (511 points) | 114 views

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