Login
Register
@
Dark Mode
Profile
Edit my Profile
Messages
My favorites
Register
Activity
Q&A
Questions
Unanswered
Tags
Subjects
Users
Ask
Previous Years
Blogs
New Blog
Exams
Dark Mode
Webpage for Linear Algebra
Recent questions tagged linear-algebra
4
votes
0
answers
31
GO Classes Test Series 2024 | Mock GATE | Test 11 | Question: 30
Let $A$ be a matrix defined as $A=u v^T$, where $u$ and $v$ are column vectors of dimension $3 \times 1$. The resulting matrix $A$ will be of dimension $3 \times 3$. What are the maximum number of nonzero eigenvalues possible for the matrix $A?$
GO Classes
asked
in
Linear Algebra
Jan 13
by
GO Classes
678
views
goclasses2024-mockgate-11
goclasses
numerical-answers
linear-algebra
eigen-value
1-mark
5
votes
1
answer
32
GO Classes Test Series 2024 | Mock GATE | Test 11 | Question: 36
Consider the system $A \mathbf{x}=\mathbf{b}$, with coefficient matrix $A$ and augmented matrix $[A \mid b]$. The sizes of $\mathbf{b}, A$, and $[A \mid \mathbf{b}]$ are $m \times 1, m \times n$ ... $\operatorname{rank}[A]>$ $\operatorname{rank}[A \mid b]$.
GO Classes
asked
in
Linear Algebra
Jan 13
by
GO Classes
446
views
goclasses2024-mockgate-11
goclasses
linear-algebra
system-of-equations
multiple-selects
2-marks
0
votes
0
answers
33
Linear Transformation of Matrix
Debargha Mitra Roy
asked
in
Linear Algebra
Jan 12
by
Debargha Mitra Roy
56
views
linear-algebra
matrix
0
votes
1
answer
34
GATE 2016 | MATHS | Q-48
Let \( M= \begin{bmatrix} 1 & 1 & 0 \\ 0 & 1 & 1 \\ 0 & 0 & 1 \end{bmatrix} \) and \( e^M = Id + M + \frac{M^2}{2!} + \frac{M^3}{3!} + \frac{M^4}{4!} + \ldots \). If \( e^M = [b_{ij}]\). then \[\frac{1}{e} \sum_{i=1}^{3} \sum_{j=1}^{3} b_{ij} \] is equal to ________________________
rajveer43
asked
in
Linear Algebra
Jan 11
by
rajveer43
137
views
linear-algebra
0
votes
0
answers
35
GATE 2016 | MATHS | QUESTION-47
Let \( A = \begin{bmatrix} a & b & c \\ b& d & e\\ c& e& f\end{bmatrix} \) be a real matrix with eigenvalues 1, 0, and 3. If the eigenvectors corresponding to 1 and 0 are \(\begin{bmatrix} 1 \\ 1 \\ 1 \end{bmatrix}\) and \(\begin{bmatrix} 1 \\ -1 \\ 0 \end{bmatrix}\) respectively, then the value of \(3f\) is equal to ________________________
rajveer43
asked
in
Linear Algebra
Jan 11
by
rajveer43
141
views
linear-algebra
0
votes
0
answers
36
GATE 2016 | MATHS | Q-12
Consider the following statements P and Q: (P) : If \( M = \begin{bmatrix} 1 & 1 & 1 \\ 1 & 2 & 4 \\ 1 & 3 & 9 \end{bmatrix} \), then M is singular. (Q) : Let S be a diagonalizable matrix. If T is a matrix such that \( ... ), then T is diagonalizable. Which of the above statements hold TRUE? (A) both P and Q (B) only P (C) only Q (D) Neither P nor Q
rajveer43
asked
in
Linear Algebra
Jan 11
by
rajveer43
80
views
linear-algebra
0
votes
0
answers
37
GATE 2016 | MATHS | Q-14
Consider a real vector space \( V \) of dimension \( n \) and a non-zero linear transformation \( T: \mathbb{V} \rightarrow \mathbb{V} \). If \( \text{dim}(T) < n \) and $T^2 = \lambda T$, for some \( \lambda \in \mathbb{R} \backslash \{0\} \), then which ... 0 \) for all \( X \in \mathbb{W} \) (C) \( T \) is invertible (D) \( \lambda\) is the only eigenvalue of \( T \)
rajveer43
asked
in
Linear Algebra
Jan 11
by
rajveer43
64
views
linear-algebra
0
votes
0
answers
38
GATE 2018 | MATHS | Q-55
Let \( A \) be a \(3 \times 3\) matrix with real entries. If three solutions of the linear system of differential equations \(\dot{x}(t) = Ax(t)\) are given by \[ \begin{bmatrix} e^t - e^{2t} \\ -e^{t} + e^{2t} \\ e^t + e^{2t} \end{bmatrix}, \begin{bmatrix} ... \\ e^{-t} - 2e^t \\ -e^{-t} + 2e^t \end{bmatrix}, \] then the sum of the diagonal entries of \( A \) is equal to
rajveer43
asked
in
Linear Algebra
Jan 11
by
rajveer43
78
views
linear-algebra
0
votes
2
answers
39
GATE 2018 | MATHS | Q-52
Consider the matrix \( A = I_9 - 2u^T u \) with \( u = \frac{1}{3}[1, 1, 1, 1, 1, 1, 1, 1, 1] \), where \( I_9 \) is the \(9 \times 9\) identity matrix and \( u^T \) is the transpose of \( u \). If \( \lambda \) and \( \mu \) are two distinct eigenvalues of \( A \), then \[ | \lambda - \mu | = \] _________
rajveer43
asked
in
Linear Algebra
Jan 11
by
rajveer43
84
views
linear-algebra
1
vote
1
answer
40
GATE 2018 | MATHS | Q-51
Consider \( \mathbb{R}^3 \) with the usual inner product. If \( d \) is the distance from \( (1, 1, 1) \) to the subspace ${(1, 1, 0), (0, 1, 1)}$ of \( \mathbb{R}^3 \), then \( 3d^2 \) is given by
rajveer43
asked
in
Linear Algebra
Jan 11
by
rajveer43
123
views
linear-algebra
vector-space
0
votes
0
answers
41
GATE 2018 | MATHS | Q-50
Let \( M_2(\mathbb{R}) \) be the vector space of all \( 2 \times 2 \) real matrices over the field \( \mathbb{R} \). Define the linear transformation \( S : M_2(\mathbb{R}) \to M_2(\mathbb{R}) \) by \( S(X) = 2X + X^T \), where \( X^T \) denotes the transpose of the matrix \( X \). Then the trace of \( S \) equals________
rajveer43
asked
in
Linear Algebra
Jan 11
by
rajveer43
54
views
linear-algebra
vector-space
0
votes
1
answer
42
GATE 2018 | MATHS | Q-42 DA Practice Questions
Consider the following two statements: \(P\): The matrix \(\begin{bmatrix} 0 & 5 \\ 0 & 7 \end{bmatrix}\) has infinitely many LU factorizations, where \(L\) is lower triangular with each diagonal entry 1 and \(U\) is upper triangular. \(Q\): The matrix \( ... \(Q\) are TRUE (C) \(P\) is FALSE and \(Q\) is TRUE (D) Both \(P\) and \(Q\) are FALSE
rajveer43
asked
in
Linear Algebra
Jan 11
by
rajveer43
151
views
linear-algebra
0
votes
0
answers
43
GATE 2018 | MATHS | Q-24
Consider the subspaces \[ W_1 = \{(x_1, x_2, x_3) \in \mathbb{R}^3 : x_1 = x_2 + 2x_3 \} \] \[ W_2 = \{(x_1, x_2, x_3) \in \mathbb{R}^3 : x_1 = 3x_2 + 2x_3 \} \] of \( \mathbb{R}^3 \). Then the dimension of \(W_1 + W_2\) equals_________
rajveer43
asked
in
Linear Algebra
Jan 11
by
rajveer43
44
views
linear-algebra
0
votes
0
answers
44
GATE 2018 | MATHS | Q-23
Let A = A = \begin{bmatrix} a & 2f & 0 \\ 2f & b & 3f \\ 0 & 3f & c \\ \end{bmatrix} , where $a, b, c, f$ are real numbers and $f not equalto0$. The geometric multiplicity of the largest eigenvalue of A equals ._______
rajveer43
asked
in
Linear Algebra
Jan 11
by
rajveer43
48
views
linear-algebra
0
votes
0
answers
45
Diagonalization of Matrix
Debargha Mitra Roy
asked
in
Linear Algebra
Jan 11
by
Debargha Mitra Roy
45
views
matrix
linear-algebra
eigen-value
0
votes
0
answers
46
Diagonalization of Matrix - Orthogonal Transformation
Consider a symmetric matrix $M=\begin{bmatrix} \frac{1}{3} & 0 & \frac{2}{3}\\ 0&1 &0 \\ \frac{2}{3}&0 & \frac{1}{3} \end{bmatrix}$. An orthogonal matrix $O$ which can diagonalize this matrix by an orthogonal transformation $O^TMO$ is given by $O = $ ______
Debargha Mitra Roy
asked
in
Linear Algebra
Jan 11
by
Debargha Mitra Roy
71
views
linear-algebra
eigen-value
matrix
0
votes
0
answers
47
GATE 2019 | Maths | DA Sample questions
Let $V$ be the vector space of all $3 \times 3$ matrices with complex entries over the real field. If $W_1 = \{A \in V : A = \bar{\mathbf{A}}^T \}$ and $W_2 = \{A \in V : trace(A)=0\}$, then the dimension of $W_1 + W_2$ is equal to ______________ ($\bar{\mathbf{A}}^T $ denotes the conjugate transpose of $A$.)
rajveer43
asked
in
Linear Algebra
Jan 10
by
rajveer43
91
views
vector-space
linear-algebra
0
votes
0
answers
48
GATE 2019 | MATHS | LINEAR ALGEBRA
Let $ \mathbf{M} $ be a $3 \times 3$ real symmetric matrix with eigenvalues $0, 2$ and $a$ with the respective eigenvectors $\mathbf{u} = \begin{bmatrix} 4 \\ b \\ c \end{bmatrix}$, $\mathbf{v} = \begin{bmatrix} -1 \\ 2 \\ 0 \end{bmatrix}$, and ... of the above statements are TRUE? (A) I, II and III only (B) I and II only (C) II and IV only (D) III and IV only
rajveer43
asked
in
Linear Algebra
Jan 10
by
rajveer43
52
views
linear-algebra
1
vote
0
answers
49
GATE 2019 | MATHS | QUESTION 40
If the characteristic polynomial and minimal polynomial of a square matrix $ \mathbf{A} $ are $(\lambda - 1)(\lambda + 1)^4 (\lambda - 2)^5$ and $(\lambda - 1)(\lambda + 1)(\lambda - 2)$ respectively, then the rank of the matrix $ \mathbf{A} + \mathbf{I} $, where $ \mathbf{I} $ is the identity matrix of the appropriate order, is________________
rajveer43
asked
in
Linear Algebra
Jan 10
by
rajveer43
60
views
linear-algebra
0
votes
0
answers
50
GATE 2021 | MATHS | QUESTION
Let $ \mathbf{A} $ be a square matrix such that $ \det(\mathbf{xI} - \mathbf{A}) = \mathbf{x}^4 (\mathbf{x} - 1)^2 (\mathbf{x} - 2)^3 $, where $ \det(\mathbf{M}) $ denotes the determinant of a square matrix $ \mathbf{M} $ ... $ 0 $ of $ \mathbf{A} $ is __________
rajveer43
asked
in
Linear Algebra
Jan 10
by
rajveer43
44
views
linear-algebra
0
votes
0
answers
51
GATE 2021 | MATHS | PRACTICE PROBLEMS FOR DA PAPER
Let $ \langle \cdot, \cdot \rangle: \mathbb{R}^n \times \mathbb{R}^n \to \mathbb{R} $ be an inner product on the vector space $ \mathbb{R}^n $ over $ \mathbb{R} $. Consider the following statements: $P:$ ... P and Q are TRUE (B) P is TRUE and Q is FALSE (C) P is FALSE and Q is TRUE (D) both P and Q are FALSE
rajveer43
asked
in
Linear Algebra
Jan 10
by
rajveer43
97
views
linear-algebra
vector-space
0
votes
0
answers
52
GATE 2021 | MATHS | Q-14
Let $ \mathbf{R} $ be the row reduced echelon form of a $ 4 \times 4 $ real matrix $ \mathbf{A} $, and let the third column of $ \mathbf{R} $ be $ \begin{bmatrix} 0 \\ 1 \\ 0 \\ 0 \end{bmatrix} $. Consider the following statements: $P:$ ... : (A) both P and Q are TRUE (B) P is TRUE and Q is FALSE (C) P is FALSE and Q is TRUE (D) both P and Q are FALSE
rajveer43
asked
in
Linear Algebra
Jan 10
by
rajveer43
47
views
linear-algebra
0
votes
0
answers
53
GATE 2021 | MATHS | Q-11
Let $ \mathbf{A} $ be a $ 3 \times 4 $ matrix and $ \mathbf{B} $ be a $ 4 \times 3 $ matrix with real entries such that $ \mathbf{A}\mathbf{B} $ is non-singular. Consider the following statements: $P:$ Nullity of $ \mathbf{A} $ is $ 0 $. $Q:$ ... Then (A)]both P and Q are TRUE (B) P is TRUE and Q is FALSE (C) P is FALSE and Q is TRUE (D) both P and Q are FALSE
rajveer43
asked
in
Linear Algebra
Jan 10
by
rajveer43
51
views
linear-algebra
0
votes
1
answer
54
GATE 2022 | MATHS | Q-65
Let M be a $3 × 3$ real matrix such that $M^2 = 2M + 3I$. If the determinant of $M$ is $−9$, then the trace of $M$ equals._______
rajveer43
asked
in
Linear Algebra
Jan 10
by
rajveer43
119
views
linear-algebra
0
votes
0
answers
55
GATE 2022 | MATHS | Q-56 SAMPLE QUESTION FOR DA
Consider \( \mathbb{R}^3 \) as a vector space with the usual operations of vector addition and scalar multiplication. Let \( x \in \mathbb{R}^3 \) be denoted by \( x = (x_1, x_2, x_3) \). Define subspaces \[ W1 := \{x \in \mathbb{R}^3 : x_1 + 2x_2 - x_3 = 0\} ... {R}^3) = 1 \) (C) \( \text{dim}(W1 + W2) = 2 \) (D) \( \text{dim}(W1 \cap W2) = 1 \)
rajveer43
asked
in
Linear Algebra
Jan 10
by
rajveer43
55
views
linear-algebra
0
votes
0
answers
56
GATE 2022 | MATHS | Q-25
Consider the linear system of equations \(Ax = b\) with \[ A = \begin{bmatrix} 3 & 1 & 1 \\ 1 & 4 & 1 \\ 2 & 0 & 3 \\ \end{bmatrix} \] and \[ b = \begin{bmatrix} 2 \\ 3 \\ 4 \\ \end ... for any initial vector. (C) The Gauss-Seidel iterative method converges for any initial vector. (D) The spectral radius of the Jacobi iterative matrix is less than 1.
rajveer43
asked
in
Linear Algebra
Jan 10
by
rajveer43
66
views
linear-algebra
matrix
0
votes
0
answers
57
GATE 2022 | Maths | Q-12
Consider $P :$ Let \( M \in \mathbb{R}^{m \times n} \) with \( m > n \geq 2 \). If \( \text{rank}(M) = n \), then the system of linear equations \( Mx = 0 \) has \( x = 0 \) as the only solution. $Q:$ Let \( E \in \mathbb{R}^{n \ ... following statements is TRUE? (A) Both P and Q are TRUE (B) Both P and Q are FALSE (C)P is TRUE and Q is FALSE (D) P is FALSE and Q is TRUE
rajveer43
asked
in
Linear Algebra
Jan 10
by
rajveer43
57
views
linear-algebra
0
votes
1
answer
58
GATE 2022 | MATHS | LINEAR ALGEBRA
Suppose that the characteristic equation of \( M \in \mathbb{C}^{3 \times 3} \) is \[ \lambda^3 + \alpha \lambda^2 + \beta \lambda - 1 = 0, \] where \( \alpha, \beta \in \mathbb{C} \) with \( \alpha + \beta \neq 0 \). Which of the following statements is TRUE? (A) \( M(I ... 1} (M^{-1} + \beta I) = M - \alpha I \) (D)\( M^{-1} (M^{-1} - \beta I) = M + \alpha I \)
rajveer43
asked
in
Linear Algebra
Jan 10
by
rajveer43
94
views
linear-algebra
0
votes
0
answers
59
GATE 2023 | Maths | Question 60
Let \( A = [a_{ij}]\) be a \(3 \times 3\) real matrix such that \[ A \begin{bmatrix} 1 \\ 2 \\ 1 \end{bmatrix} = 2 \begin{bmatrix} 1 \\ 2 \\ 1 \end{bmatrix}, \quad A \begin{bmatrix} 0 \\ 1 \\ 1 \end{bmatrix} = 2 \begin{bmatrix} 0 \\ 1 ... is the degree of the minimal polynomial of \( A \), then \( a_{11} + a_{21} + a_{31} + m \) equals \(\underline{\hspace{1cm}}\).
rajveer43
asked
in
Linear Algebra
Jan 10
by
rajveer43
64
views
linear-algebra
Page:
« prev
1
2
3
4
5
6
7
...
27
next »
Subscribe to GATE CSE 2024 Test Series
Subscribe to GO Classes for GATE CSE 2024
Quick search syntax
tags
tag:apple
author
user:martin
title
title:apple
content
content:apple
exclude
-tag:apple
force match
+apple
views
views:100
score
score:10
answers
answers:2
is accepted
isaccepted:true
is closed
isclosed:true
Recent Posts
Post GATE 2024 Guidance [Counseling tips and resources]
GATE CSE 2024 Result Responses
[Project Contest] Pytorch backend support for MLCommons Cpp Inference implementation
Participating in MLCommons Inference v4.0 submission (deadline is February 23 12pm IST)
IIITH PGEE 2024 Test Series by GO Classes
Subjects
All categories
General Aptitude
(3.5k)
Engineering Mathematics
(10.4k)
Digital Logic
(3.6k)
Programming and DS
(6.2k)
Algorithms
(4.8k)
Theory of Computation
(6.9k)
Compiler Design
(2.5k)
Operating System
(5.2k)
Databases
(4.8k)
CO and Architecture
(4.0k)
Computer Networks
(4.9k)
Artificial Intelligence
(79)
Machine Learning
(48)
Data Mining and Warehousing
(24)
Non GATE
(1.4k)
Others
(2.7k)
Admissions
(682)
Exam Queries
(1.6k)
Tier 1 Placement Questions
(17)
Job Queries
(80)
Projects
(11)
Unknown Category
(870)
64.3k
questions
77.9k
answers
243k
comments
79.6k
users
Recent questions tagged linear-algebra
Recent Blog Comments
Hlo I'm Rupesh I got AIR 3485 in gate CS and AIR...
@Ajay Sasank here is the direct link...
Thank you for the post didi My GATE 2023 & 2024...
I Hope it helps 😊
Today's best post I seen thank you for motivation