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Recent questions and answers in Linear Algebra

56 votes

8 answers

1

GATE CSE 2017 Set 1 | Question: 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 $Ax = b$ ... 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

-RahulKumar- answered in Linear Algebra 1 day ago

by -RahulKumar-

15.4k views

10 votes

3 answers

2

GATE CSE 2021 Set 1 | Question: 52
Consider the following matrix.$\begin{pmatrix} 0 & 1 & 1 & 1\\ 1& 0& 1 & 1\\ 1& 1 & 0 & 1 \\1 & 1 & 1 & 0 \end{pmatrix}$The largest eigenvalue of the above matrix is __________.

Sai8 answered in Linear Algebra 4 days ago

by Sai8

8.4k views

31 votes

8 answers

3

GATE CSE 2021 Set 2 | Question: 24
Suppose that $P$ is a $4 \times 5$ matrix such that every solution of the equation $\text{Px=0}$ is a scalar multiple of $\begin{bmatrix} 2 & 5 & 4 &3 & 1 \end{bmatrix}^T$. The rank of $P$ is __________

ArturoGangwar answered in Linear Algebra 5 days ago

by ArturoGangwar

10.0k views

4 votes

2 answers

4

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

39Gaurav_singh answered in Linear Algebra Mar 20

by 39Gaurav_singh

2.5k views

3 votes

4 answers

5

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

39Gaurav_singh answered in Linear Algebra Mar 20

by 39Gaurav_singh

1.2k views

26 votes

5 answers

6

GATE CSE 2017 Set 1 | Question: 30
Let $u$ and $v$ be two vectors in $\mathbf{R}^{2}$ whose Euclidean norms satisfy $\left \| u \right \| = 2\left \| v \right \|$. What is the value of $\alpha$ such that $w = u + \alpha v$ bisects the angle between $u$ and $v$? $2$ $\frac{1}{2}$ $1$ $\frac{ -1}{2}$

KG answered in Linear Algebra Mar 19

by KG

11.3k views

0 votes

1 answer

7

#self_doubt
if the determinant of matrix A is d then the determinant of the cofactor matrix of A will be d^2, is this rule correct? I am not able to satisfy this rule with a 2*2 matrix.

Amartya007 answered in Linear Algebra Mar 15

47 views

8 votes

4 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 $\{n,1\}$ $\{n,n\}$ $\{n^2,1\}$ $\{1,n^2\}$

anirudhkumar18 answered in Linear Algebra Mar 14

by anirudhkumar18

5.0k views

0 votes

2 answers

9

Engineering mathematics
If A is a non-zero column matrix of order n×1 and B is a non-zero row matrix of order 1×n then rank of AB equals ? Rank(ab) can be zero???

Ujjal roy answered in Linear Algebra Mar 8

216 views

0 votes

1 answer

10

MADEEASY TESTSERIES
To justify the OPTION B they gave an example of 2*2 matrix. However we can see that row 2 is linearly dependent on row1. Even though the 2nd row looks non-zero it can be made into zero. SO am I wrong or the explanation is wrong?

Ujjal roy answered in Linear Algebra Mar 8

176 views

0 votes

0 answers

11

Numerical Method Analysis : Help...
Use LU Decomposition method to solve the following system. $\left\{\begin{matrix} & x_{1} +x_{2}-x_{3} =1 \\ & x_{1} +2x_{2}-2x_{3} =0 \\ & -2x_{1} +x_{2}+x_{3} =1 \end{matrix}\right.$ ...

kidussss asked in Linear Algebra Mar 8

43 views

0 votes

0 answers

12

Numerical Method Analysis : Help...
Solve the following system using Gauss elimination with partial pivoting. $\left\{\begin{matrix} &2x_{1}+x_{2}+x_{3}=10\\ & 3x_{1}+2x_{2}+3x_{3}=18 \\ & 5x_{1}+4x_{2}+2x_{3}=9 \end{matrix}\right.$ ...

kidussss asked in Linear Algebra Mar 8

30 views

0 votes

0 answers

13

Numerical Method Analysis : Help...
Use Secant method to find roots of: $x^3-2x^2+3x-5=0$ $x+1 = 4sinx$ $e^x = x + 2$

kidussss asked in Linear Algebra Mar 8

29 views

0 votes

0 answers

14

Numerical Method Analysis : Help....
Use NR method to find a root of the equation with tolerance x=0.00001. $x^3-2x-5=0$ $e^x-3x^2=0$

kidussss asked in Linear Algebra Mar 8

21 views

0 votes

0 answers

15

Numerical Method Analysis : Help...
Use Bisection method to find all roots of $x^3 – 5x + 3 = 0$

kidussss asked in Linear Algebra Mar 8

34 views

0 votes

0 answers

16

Numerical Method Analysis : Help...
Use Bisection method to find the root of the following equation with tolerance 0.001. $x^4 - 2x^3 - 4x^2 + 4x + 4 = 0$ $x^3 – e^x + sin(x) = 0$

kidussss asked in Linear Algebra Mar 8

39 views

14 votes

4 answers

17

GATE CSE 2022 | Question: 35
Consider solving the following system of simultaneous equations using $\text{LU}$ decomposition. $x_{1} + x_{2} - 2x_{3} = 4$ $x_{1} + 3x_{2} - x_{3} = 7$ $2x_{1} + x_{2} - 5x_{3} = 7$ where $\textit{L}$ and $\textit{U}$ ... $\textit{L}_{32}= - \frac{1}{2}, \textit{U}_{33}= - \frac{1}{2}, x_{1}= 0$

Mukulvyas answered in Linear Algebra Mar 3

4.4k views

3 votes

2 answers

18

GATE CSE 2023 | Question: 8
Let \[ A=\left[\begin{array}{llll} 1 & 2 & 3 & 4 \\ 4 & 1 & 2 & 3 \\ 3 & 4 & 1 & 2 \\ 2 & 3 & 4 & 1 \end{array}\right] \] and \[ B=\left[\begin{array}{llll} 3 & 4 & ... $\operatorname{det}(B)=-\operatorname{det}(A)$ $\operatorname{det}(A)=0$ $\operatorname{det}(A B)=\operatorname{det}(A)+\operatorname{det}(B)$

admin asked in Linear Algebra Feb 15

by admin

980 views

2 votes

2 answers

19

GATE CSE 2023 | Question: 20
Let $A$ be the adjacency matrix of the graph with vertices $\{1,2,3,4,5\}.$ Let $\lambda_{1}, \lambda_{2}, \lambda_{3}, \lambda_{4}$, and $\lambda_{5}$ be the five eigenvalues of $A$. Note that these eigenvalues need not be distinct. The value of $\lambda_{1}+\lambda_{2}+\lambda_{3}+\lambda_{4}+\lambda_{5}=$____________

admin asked in Linear Algebra Feb 15

by admin

1.4k views

2 votes

1 answer

20

GATE CSE 2023 | Memory Based Question: 13
Let $ A=\left[\begin{array}{llll} 1 & 2 & 3 & 4 \\ 4 & 1 & 2 & 3 \\ 3 & 4 & 1 & 2 \\ 2 & 3 & 4 & 1 \end{array}\right] $ ... $\operatorname{det} \mathrm{B}=-\operatorname{det} \mathrm{A}$ $\operatorname{det} \mathrm{A}=\operatorname{det} \mathrm{B}$

GO Classes asked in Linear Algebra Feb 6

497 views

0 votes

0 answers

21

Linear Algebra, Vectors
What is the equation of the plane that contains point (-2, 4, 5) and the vector (7, 0, -6) is normal to the plane? And check if this plane intersects the y-axis.

kidussss asked in Linear Algebra Jan 13

103 views

0 votes

0 answers

22

Linear Algebra, Vectors
Find equation of a line passes through the points = (0, 1, 2) and = (-1, 1, 1).

kidussss asked in Linear Algebra Jan 13

75 views

0 votes

0 answers

23

ZEAL TEST
Isn’t the “No of independent rows”= RAnk of matrix?

DAWID15 asked in Linear Algebra Jan 8

202 views

0 votes

0 answers

24

Self Doubt
Question: How NullSpace of the matrix A and the uniqueness of the solution of Ax=b are related ??

lalitver10 asked in Linear Algebra Dec 24, 2022

106 views

1 vote

1 answer

25

DRDO CSE 2022 Paper 1 | Question: 1
Compute $\left[M M^{T}\right]^{-1}$ for an orthogonal matrix where \[M=\left[\begin{array}{lll} \frac{1}{\sqrt{2}} & \frac{2}{\sqrt{2}} & \frac{-2}{\sqrt{2}} \\ \frac{-2}{\sqrt{2}} & \frac{2}{\sqrt{2}} & \frac{1}{\sqrt{2}} \\ \frac{2}{\sqrt{2}} & \frac{1}{\sqrt{2}} & \frac{2}{\sqrt{2}} \end{array}\right] .\]

admin asked in Linear Algebra Dec 15, 2022

by admin

108 views

1 vote

0 answers

26

DRDO CSE 2022 Paper 1 | Question: 2
Calculate the eigenvalues of matrix $M, M^{-1}, M^{2}$ and $M+2 I$ where \[M=\left[\begin{array}{cc} 4 & 5 \\ 2 & -5 \end{array}\right].\]

admin asked in Linear Algebra Dec 15, 2022

by admin

57 views

1 vote

0 answers

27

DRDO CSE 2022 Paper 1 | Question: 3
With no unique solution, solve for $n$ with the following system of equations $\begin{array}{r} a+b+2 c=3 \\ a+2 b+3 c=4 \\ a+4 b+n c=6 \end{array}$

admin asked in Linear Algebra Dec 15, 2022

by admin

83 views

0 votes

0 answers

28

#LinearAlgebra
Is this correct?

robinofautumn asked in Linear Algebra Nov 24, 2022

by robinofautumn

102 views

0 votes

0 answers

29

TIFR system Science 2017 question 7
A circulant matrix is a square matrix whose each row is the preceding row rotated to the right by one element, e.g., the following is a 3 3 circulant matrix \begin{pmatrix} 1 & 2 & 3\\ 3 & 1 & 2\\ 2 & 3 & 1 \end{pmatrix} For any ... $j = \sqrt{−1}$ (d) A vector whose k-th element is $\sin h (2πk/n)$ (e) None of the above

analyse asked in Linear Algebra Nov 22, 2022

107 views

0 votes

0 answers

30

Matrix
While studying Linear algebra I got 2 perspectives. Which meaning out of these 2 is more accurate?

Mohib asked in Linear Algebra Oct 17, 2022

by Mohib

150 views

2 votes

2 answers

31

Made Easy: Linear Algebra (MSQ)
Let $A$ be a $3$ x $3$ matrix with rank $2$. Then, $AX=0$ has The trivial solution $X=0$. One independent solution. Two independent solution. Three independent solution.

DebRC asked in Linear Algebra Sep 19, 2022

by DebRC

436 views

1 vote

0 answers

32

Self doubt.
If A, B & C are matrices & AB=AC then B=C? as we know it is not always true because when A is singular matrix then B=C not possible so what is the right ans to say B=C is (always not equal) or (may or may not be equal) or (simply not equal)?

Nisha Bharti asked in Linear Algebra Sep 19, 2022

by Nisha Bharti

203 views

0 votes

0 answers

33

Eigen Value Of A Matrix
For given Matrix: [ 1 2 3 1 5 1 3 1 1 ] Why does the sum of the eigen values of above matrix is the sum of diagonal elements of that matrix?

ryandany07 asked in Linear Algebra Sep 4, 2022

163 views

1 vote

0 answers

34

TIFR CSE 2022 | Part B | Question: 15
Let $\mathbb{R}$ denote the set of real numbers. Let $d \geq 4$ and $\alpha \in \mathbb{R}$ ... $\left(a_0, a_1, \ldots, a_d\right) \in S$, the function $ x \mapsto \sum_{i=0}^d a_i x^i $ has a local optimum at $\alpha$

admin asked in Linear Algebra Sep 1, 2022

by admin

161 views

1 vote

1 answer

35

TIFR CSE 2022 | Part A | Question: 4
Consider the polynomial $p(x)=x^3-x^2+x-1$. How many symmetric matrices with integer entries are there whose characteristic polynomial is $p$? (Recall that the characteristic polynomial of a square matrix $A$ in the variable $x$ is defined to be the determinant of the matrix $(A-x I)$ where $I$ is the identity matrix.) $0$ $1$ $2$ $4$ Infinitely many

Lakshman Patel RJIT asked in Linear Algebra Sep 1, 2022

by Lakshman Patel RJIT

245 views

13 votes

1 answer

36

TIFR CSE 2022 | Part A | Question: 8
Let $A$ be the $(n+1) \times(n+1)$ matrix given below, where $n \geq 1$. For $i \leq n$, the $i$-th row of $A$ has every entry equal to $2i-1$ and the last row, i.e., the $(n+1)$-th row of $A$ has every entry equal to $-n^2$ ... $A$ has rank $n$ $A^2$ has rank $1$ All the eigenvalues of $A$ are distinct All the eigenvalues of $A$ are $0$ None of the above

Lakshman Patel RJIT asked in Linear Algebra Sep 1, 2022

by Lakshman Patel RJIT

317 views

0 votes

1 answer

37

ISI 2020 | PCB Mathematics | Question: 3
Suppose $A$ is an $(n \times n)$ matrix over $\mathbb{R}$ such that $A^{p}=0$ for some positive integer $p$. Prove that $I+A$ is an invertible matrix, where $I$ is the $(n \times n)$ identity matrix. Find the characteristic polynomial of $A$.

Lakshman Patel RJIT asked in Linear Algebra Aug 8, 2022

by Lakshman Patel RJIT

89 views

1 vote

1 answer

38

GATE-2014 EC
Which one of the following statements is NOT true for a square matrix A? If A is real symmetric, the eigen values of A are the diagonal elements of it. If all the principal minors of A are positive, all the eigen values of A are also positive. My question is what is “principal minors of A” ?

samarpita asked in Linear Algebra May 9, 2022

285 views

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Recent questions and answers in Linear Algebra