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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
gatecse-2017-set1
linear-algebra
system-of-equations
normal
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
gatecse-2021-set1
linear-algebra
matrix
eigen-value
numerical-answers
2-marks
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
gatecse-2021-set2
numerical-answers
linear-algebra
matrix
rank-of-matrix
1-mark
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
engineering-mathematics
linear-algebra
matrix
rank-of-matrix
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
isi2018-mma
engineering-mathematics
linear-algebra
rank-of-matrix
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
gatecse-2017-set1
linear-algebra
normal
vector-space
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
by
Amartya007
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
isrodec2017
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
by
Ujjal roy
216
views
engineering-mathematics
linear-algebra
matrix
self-doubt
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
by
Ujjal roy
176
views
made-easy-test-series
matrix
linear-algebra
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
by
kidussss
43
views
numerical-methods
algorithms
discrete-mathematics
linear-algebra
engineering-mathematics
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
by
kidussss
30
views
numerical-methods
algorithms
linear-algebra
engineering-mathematics
discrete-mathematics
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
by
kidussss
29
views
numerical-methods
algorithms
discrete-mathematics
linear-algebra
engineering-mathematics
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
by
kidussss
21
views
numerical-methods
algorithms
discrete-mathematics
linear-algebra
engineering-mathematics
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
by
kidussss
34
views
numerical-methods
algorithms
linear-algebra
engineering-mathematics
discrete-mathematics
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
by
kidussss
39
views
numerical-methods
algorithms
linear-algebra
engineering-mathematics
discrete-mathematics
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
by
Mukulvyas
4.4k
views
gatecse-2022
linear-algebra
matrix
system-of-equations
2-marks
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
gatecse-2023
linear-algebra
determinant
1-mark
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
gatecse-2023
linear-algebra
eigen-value
numerical-answers
1-mark
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
by
GO Classes
497
views
memorybased-gatecse2023
goclasses
linear-algebra
determinant
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
by
kidussss
103
views
linear-algebra
engineering-mathematics
vector-space
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
by
kidussss
75
views
linear-algebra
engineering-mathematics
0
votes
0
answers
23
ZEAL TEST
Isn’t the “No of independent rows”= RAnk of matrix?
DAWID15
asked
in
Linear Algebra
Jan 8
by
DAWID15
202
views
zeal
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
by
lalitver10
106
views
self-doubt
linear-algebra
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
drdocse-2022-paper1
linear-algebra
matrix
3-marks
descriptive
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
drdocse-2022-paper1
linear-algebra
eigen-value
5-marks
descriptive
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
drdocse-2022-paper1
linear-algebra
system-of-equations
5-marks
descriptive
0
votes
0
answers
28
#LinearAlgebra
Is this correct?
robinofautumn
asked
in
Linear Algebra
Nov 24, 2022
by
robinofautumn
102
views
linear-algebra
eigen-value
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
by
analyse
107
views
eigen-value
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
matrix
linear-algebra
engineering-mathematics
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
linear-algebra
engineering-mathematics
rank-of-matrix
matrix
system-of-equations
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
matrix
determinant
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
by
ryandany07
163
views
eigen-value
matrix
engineering-mathematics
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
tifr2022
linear-algebra
vector-space
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
tifr2022
linear-algebra
matrix
determinant
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
tifr2022
linear-algebra
rank-of-matrix
eigen-value
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
isi2020-pcb-mathematics
descriptive
linear-algebra
matrix
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
by
samarpita
285
views
linear-algebra
gate2014-ec-1
eigen-value
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Recent questions and answers in Linear Algebra
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