Recent questions tagged linear-algebra

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1

Linear Algebra (Self Doubt)
Let $A$ be a $n \times n$ square matrix whose all columns are independent. Is $Ax = b$ always solvable? Actually, I know that $Ax= b$ is solvable if $b$ is in the column space of $A$. However, I am not sure if it is solvable for all values of $b$.

asked Jun 6 in Linear Algebra by Debargha Bhattacharj Junior (515 points) | 75 views

0 votes

2 answers

2

GATE 2017:EC
Consider the $5\times 5$ matrix: $\begin{bmatrix} 1 & 2 &3 & 4 &5 \\ 5 &1 &2 & 3 &4 \\ 4& 5 &1 &2 &3 \\ 3& 4 & 5 & 1 &2 \\ 2&3 & 4 & 5 & 1 \end{bmatrix}$ It is given $A$ has only one real eigen value. Then the real eigen value of $A$ is ________

asked Jun 2 in Linear Algebra by srestha Veteran (113k points) | 106 views

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0 answers

3

GATE MOCK 2018
An orthogonal matrix A has eigen values 1, 2 and 4, then trace of the matrix $A^T$ is ___________

asked May 28 in Linear Algebra by Hirak Active (3.4k points) | 58 views

0 votes

1 answer

4

Self-Doubt: Diagonalizable Matrix
$1)$ How to find a matrix is diagonalizable or not? Suppose a matrix is $A=\begin{bmatrix} \cos \Theta &\sin \Theta \\ \sin\Theta & -\cos\Theta \end{bmatrix}$ Is it diagonalizable? $2)$ What is it’s eigen spaces?

asked May 27 in Linear Algebra by srestha Veteran (113k points) | 120 views

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0 answers

5

Self Doubt-LA
In a non-homogeneous equation Ax = b, x has a unique solution when $A^{-1}$ exists i.e x = $A^{-1}$b but when det(A) = 0 then we have infinite solution or many solution. please give a mathematical explanation of how the 2nd statement occurs?

asked May 26 in Mathematical Logic by MRINMOY_HALDER Active (1.7k points) | 34 views

+4 votes

0 answers

6

IISc CSA - Research Interview Question
Prove that the rank of the Adjacency Matrix which is associated with a $k-$ regular graph is $k.$

asked May 22 in Graph Theory by ankitgupta.1729 Boss (14k points) | 80 views

+1 vote

1 answer

7

ISI2018-PCB-A1
Consider a $n \times n$ matrix $A=I_n-\alpha\alpha^T$, where $I_n$ is the $n\times n$ identity matrix and $\alpha$ is an $n\times 1$ column vector such that $\alpha^T\alpha=1$.Show that $A^2=A$.

asked May 12 in Linear Algebra by akash.dinkar12 Boss (41.3k points) | 59 views

0 votes

1 answer

8

ISI2018-MMA-14
Let $A$ be a $3× 3$ real matrix with all diagonal entries equal to $0$. If $1 + i$ is an eigenvalue of $A$, the determinant of $A$ equals $-4$ $-2$ $2$ $4$

asked May 11 in Linear Algebra by akash.dinkar12 Boss (41.3k points) | 59 views

0 votes

1 answer

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ISI2018-MMA-13
If $A =\begin{bmatrix} 2 &i \\ i & 0 \end{bmatrix}$ , the trace of $A^{10}$ is $2$ $2(1+i)$ $0$ $2^{10}$

asked May 11 in Linear Algebra by akash.dinkar12 Boss (41.3k points) | 51 views

0 votes

2 answers

10

ISI2018-MMA-12
The rank of the matrix $\begin{bmatrix} 1 &2 &3 &4 \\ 5& 6 & 7 & 8 \\ 6 & 8 & 10 & 12 \\ 151 & 262 & 373 & 484 \end{bmatrix}$ $1$ $2$ $3$ $4$

asked May 11 in Linear Algebra by akash.dinkar12 Boss (41.3k points) | 74 views

0 votes

1 answer

11

ISI2018-MMA-11
The value of $\lambda$ for which the system of linear equations $2x-y-z=12$, $x-2y+z=-4$ and $x+y+\lambda z=4$ has no solution is $2$ $-2$ $3$ $-3$

asked May 11 in Numerical Ability by akash.dinkar12 Boss (41.3k points) | 60 views

+1 vote

1 answer

12

ISI2019-MMA-23
Let $A$ be $2 \times 2$ matrix with real entries. Now consider the function $f_A(x)$ = $Ax$ . If the image of every circle under $f_A$ is a circle of the same radius, then A must be an orthogonal matrix A must be a symmetric matrix A must be a skew-symmetric matrix None of the above must necessarily hold

asked May 7 in Linear Algebra by Sayan Bose Loyal (7k points) | 120 views

0 votes

2 answers

13

ISI2019-MMA-15
The rank of the matrix $\begin{bmatrix} 0 &1 &t \\ 2& t & -1\\ 2& 2 & 0 \end{bmatrix}$ equals $3$ for any real number $t$ $2$ for any real number $t$ $2$ or $3$ depending on the value of $t$ $1,2$ or $3$ depending on the value of $t$

asked May 7 in Linear Algebra by Sayan Bose Loyal (7k points) | 152 views

+1 vote

1 answer

14

ISI2019-MMA-14
If the system of equations $\begin{array} ax +y+z= 0 \\ x+by +z = 0 \\ x+y + cz = 0 \end{array}$ with $a,b,c \neq 1$ has a non trivial solutions, the value of $\frac{1}{1-a} + \frac{1}{1-b} + \frac{1}{1-c}$ is $1$ $-1$ $3$ $-3$

asked May 7 in Linear Algebra by Sayan Bose Loyal (7k points) | 123 views

0 votes

2 answers

15

ISI2019-MMA-13
Let $V$ be the vector space of all $4 \times 4$ matrices such that the sum of the elements in any row or any column is the same. Then the dimension of $V$ is $8$ $10$ $12$ $14$

asked May 6 in Linear Algebra by Sayan Bose Loyal (7k points) | 180 views

+1 vote

0 answers

16

CSIR UGC NET

asked Apr 28 in Linear Algebra by Hirak Active (3.4k points) | 41 views

+3 votes

1 answer

17

Vani Institute Question Bank Pg-231 chapter 6
The Eigen values of $A=\begin{bmatrix} a& 1& 0\\1 &a &1 \\0 &1 &a \end{bmatrix}$ are______ $a,a,a$ $0,a,2a$ $-a,2a,2a$ $a,a+\sqrt{2},a-\sqrt{2}$

asked Apr 25 in Linear Algebra by Hirak Active (3.4k points) | 88 views

0 votes

0 answers

18

ISI-MMA-2015-44
Let $P_{1},P_{2},$ and $P_{3}$ denote, respectively, the planes defined by $a_{1}x + b_{1}y + c_{1}z = \alpha _{1}$ $a_{2}x + b_{2}y + c_{2}z = \alpha _{2}$ $a_{3}x + b_{3}y + c_{3}z = \alpha _{3}$ It is given ... then the planes (A) do not have any common point of intersection (B) intersect at a unique point (C) intersect along a straight line (D) intersect along a plane

asked Feb 22 in Linear Algebra by ankitgupta.1729 Boss (14k points) | 84 views

+3 votes

4 answers

19

GATE2019-9
Let $X$ be a square matrix. Consider the following two statements on $X$. $X$ is invertible Determinant of $X$ is non-zero Which one of the following is TRUE? I implies II; II does not imply I II implies I; I does not imply II I does not imply II; II does not imply I I and II are equivalent statements

asked Feb 7 in Linear Algebra by Arjun Veteran (416k points) | 1.8k views

+3 votes

3 answers

20

GATE2019-44
Consider the following matrix: $R = \begin{bmatrix} 1 & 2 & 4 & 8 \\ 1 & 3 & 9 & 27 \\ 1 & 4 & 16 & 64 \\ 1 & 5 & 25 & 125 \end{bmatrix}$ The absolute value of the product of Eigen values of $R$ is _______

asked Feb 7 in Linear Algebra by Arjun Veteran (416k points) | 2.4k views

+1 vote

1 answer

21

Nullity of matrix
Nullity of a matrix = Total number columns – Rank of that matrix By how to calculate value of x when nullity is already given(1 in this case)

asked Jan 24 in Linear Algebra by Nandkishor3939 Active (1.1k points) | 137 views

0 votes

1 answer

22

Simple Determinant
how to prove determinant 1 and 2 are same by some row-column manipulation ,please Help??

asked Jan 19 in Linear Algebra by BHASHKAR (25 points) | 58 views

0 votes

1 answer

23

Made Easy Workbook
Let A be a 3*3 matrix whose characteristics roots are 3,2,-1. If $B=A^2-A$ then |B|=? a)24 b)-2 c)12 d)-12 Please explain in detail.

asked Jan 19 in Linear Algebra by Reshu $ingh (253 points) | 124 views

0 votes

1 answer

24

GATEBOOK-2019 Mock Test1-12
All the four entries of $2\times 2$ matrix $P = \begin{vmatrix} p_{11} \quad p_{12} \\ p_{21} \quad p_{22} \end{vmatrix}$ are non zero , and one of its eigen values is zero. Which of the following statements is TRUE? $p_{11}p_{22} - p_{12}p_{21} = 1$ $p_{11}p_{22} - p_{12}p_{21} = -1$ $p_{11}p_{22} - p_{12}p_{21} = 0$ $p_{11}p_{22} + p_{12}p_{21} = 0$

asked Jan 19 in Others by GATEBOOK Boss (11.4k points) | 88 views

0 votes

1 answer

25

MadeEasy Full Length Test 2019: Engineering Mathematics - Linear Algebra

asked Jan 16 in Linear Algebra by roman_1997 (169 points) | 85 views

0 votes

0 answers

26

Recurrence Relation for Array
A two dimensional array is stored in column major form in memory if the elements are stored in the following sequence ... calculated as the column number of the element we are looking for summing with the $row \times column$ number of elements. How does the above recurrence relation work?

asked Jan 7 in DS by kauray (203 points) | 85 views

0 votes

0 answers

27

Doubt on syllabus
Is LU decomposition in course for GATE 2019?

asked Jan 6 in Linear Algebra by subho16 (135 points) | 53 views

0 votes

0 answers

28

Eigen Values Doubt
Let there is a 2*2 Matrix and their eigen values are A and B. The eigen values of $(A+7I)^{-1}$ ?

asked Jan 4 in Linear Algebra by Shamim Ahmed Active (2.3k points) | 97 views

0 votes

0 answers

29

The time complexity for the possible ways of multiplying the given set of n matrices.

asked Jan 1 in Algorithms by susgir2 Active (1.4k points) | 45 views

0 votes

0 answers

30

doubt
how can we find factor of determinant by hit and trial method ? Please explain the steps https://gateoverflow.in/ask?cat=33

asked Dec 26, 2018 in Linear Algebra by Satbir Boss (17.3k points) | 21 views

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