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
13
votes
2
answers
151
GO Classes Weekly Quiz 6 | Linear Algebra | Question: 13
Given the following matrix: $ A=\left[\begin{array}{lll} 1 & 2 & 2 \\ 2 & 1 & 2 \\ 2 & 2 & 1 \end{array}\right] $ Consider the following statements: $A^2-4 A-5 I=0$ (where $I$ is identity matrix ... the following options is correct? Only $I$ is true. Only II is true. Both I and II are true. Neither I, nor II are true.
GO Classes
asked
in
Linear Algebra
Mar 29, 2023
by
GO Classes
834
views
goclasses2024_wq6
goclasses
linear-algebra
determinant
1-mark
22
votes
2
answers
152
GO Classes Weekly Quiz 6 | Linear Algebra | Question: 14
Mark all the INCORRECT statements Let $A$ be the matrix of a rotation by angle $30$ degree. That is, for any vector $x,$ the angle between $x$ and $A x$ is always $30$ degree. Then $A$ has no real eigenvalues. Let $A$ ... eigenvalues $\lambda=1,2,3$, then $A$ is singular. If $A$ is a symmetric matrix, then all its eigenvectors are orthogonal.
GO Classes
asked
in
Linear Algebra
Mar 29, 2023
by
GO Classes
1.1k
views
goclasses2024_wq6
goclasses
linear-algebra
eigen-value
multiple-selects
1-mark
17
votes
4
answers
153
GO Classes Weekly Quiz 6 | Linear Algebra | Question: 15
Suppose $\mathbf{A}=\mathbf{B C}$, where $\mathbf{B}$ is a $4 \times 2$ matrix and $\mathbf{C}$ is a $2 \times 4$ matrix. Is $\mathbf{A}$ invertible? Yes, $\mathbf{A}$ is invertible. No, $\mathbf{A}$ is not invertible. Depends on $\mathbf{C}$ only. Depends on $\mathbf{B}$ and $\mathbf{C}$.
GO Classes
asked
in
Linear Algebra
Mar 29, 2023
by
GO Classes
1.0k
views
goclasses2024_wq6
goclasses
linear-algebra
determinant
1-mark
6
votes
1
answer
154
GO Classes Weekly Quiz 6 | Linear Algebra | Question: 16
Let $A=\left[\begin{array}{cc}1 & 0 \\ -1 & 1 \\ k & 2\end{array}\right]$ and $b=\left[\begin{array}{l}1 \\ 0 \\ 1\end{array}\right]$. For which value of $k$ does the system $A \mathbf{x}=b$ have a unique solution? There is no such value for $k$. $k=0$ $k=-1$ $k=1$
GO Classes
asked
in
Linear Algebra
Mar 29, 2023
by
GO Classes
686
views
goclasses2024_wq6
goclasses
linear-algebra
system-of-equations
1-mark
9
votes
1
answer
155
GO Classes Weekly Quiz 6 | Linear Algebra | Question: 17
Let $A$ be an $m \times n$-matrix and let $B$ be an $n \times m$-matrix. Then which of the following statement is not true for all such matrices? $B A$ is defined the columns of $A B$ are linear combinations of the columns of $B$ $A B$ is defined the columns of $A B$ are linear combinations of the columns of $A$
GO Classes
asked
in
Linear Algebra
Mar 29, 2023
by
GO Classes
686
views
goclasses2024_wq6
goclasses
linear-algebra
vector-space
1-mark
6
votes
1
answer
156
GO Classes Weekly Quiz 6 | Linear Algebra | Question: 18
Consider $A=\left[\begin{array}{ll}1 & 0 \\ 0 & 1 \\ 0 & 2\end{array}\right]$ and $B=\left[\begin{array}{ccc}1 & 0 & 0 \\ 0 & 1 & -1 \\ 0 & 2 & 0\end{array}\right]$ ... $B$. $\boldsymbol{v}$ is neither a linear combination of the columns of $A$ nor of the columns of $B$.
GO Classes
asked
in
Linear Algebra
Mar 29, 2023
by
GO Classes
486
views
goclasses2024_wq6
goclasses
linear-algebra
vector-space
1-mark
7
votes
1
answer
157
GO Classes Weekly Quiz 6 | Linear Algebra | Question: 19
Let $A$ be a $2 \times 3$-matrix and $b$ a vector in $\mathbb{R}^2$. Consider the following two statements: $(\text{P}1)\; A$ has at most two pivots, $(\text{P2})$ Assuming $A x=b$ has a solution, then it has ... $\text{P2}$ is correct. Only Statement $\text{P1}$ is correct. Statement $\text{P1}$ and Statement $\text{P2}$ are correct.
GO Classes
asked
in
Linear Algebra
Mar 29, 2023
by
GO Classes
475
views
goclasses2024_wq6
goclasses
linear-algebra
system-of-equations
1-mark
17
votes
2
answers
158
GO Classes Weekly Quiz 6 | Linear Algebra | Question: 20
Suppose $A$ is $3$ by $4,$ and $A x=0$ has all solutions in the following form - $ \mathrm{x}=\mathrm{s}\left[\begin{array}{l} 1 \\ 1 \\ 1 \\ 0 \end{array}\right]+\mathrm{t}\left[\begin{array}{r} -2 \\ -1 \\ 0 \\ 1 \end{array}\right] $ ... $a, b, c,$ and $d?$ $a=-1$ $b=2$ $c=-1$ $d=1$
GO Classes
asked
in
Linear Algebra
Mar 29, 2023
by
GO Classes
714
views
goclasses2024_wq6
goclasses
linear-algebra
system-of-equations
multiple-selects
1-mark
12
votes
1
answer
159
GO Classes Weekly Quiz 6 | Linear Algebra | Question: 21
Consider a matrix $A$ of dimension $m \times n$ such that - $A x=\left[\begin{array}{l}1 \\ 1 \\ 1\end{array}\right]$ has no solutions and $A x=\left[\begin{array}{l}0 \\ 1 \\ 0\end{array}\right]$ has exactly one solution Which of the following CAN be true? $\operatorname{Rank}(A)=2$ $m=3$ $n=1$ $\operatorname{Rank}(A)=1$
GO Classes
asked
in
Linear Algebra
Mar 29, 2023
by
GO Classes
732
views
goclasses2024_wq6
goclasses
linear-algebra
system-of-equations
multiple-selects
2-marks
13
votes
3
answers
160
GO Classes Weekly Quiz 6 | Linear Algebra | Question: 22
A three-by-three matrix $B$ is known to have eigenvalues $0,1$ and $2.$ This information is enough to find which one of these (give the answers where possible): The rank of $B$ The determinant of $B^T B$ The eigenvalues of $B^T B$ The eigenvalues of $\left(B^2+I\right)^{-1}$
GO Classes
asked
in
Linear Algebra
Mar 29, 2023
by
GO Classes
1.1k
views
goclasses2024_wq6
goclasses
linear-algebra
eigen-value
multiple-selects
2-marks
23
votes
2
answers
161
GO Classes Weekly Quiz 6 | Linear Algebra | Question: 23
Let $A$ be an $m \times n$-matrix. Consider the system of linear equations $A X=b$, which of the following statement is always true: Suppose $m>n$ then rank of augmented matrix $(A \mid b)$ can not larger than $m$. Suppose $A$ ... a solution then $A X=0$ has unique solution. If $A X=b$ has a unique solution then $A$ has to be invertible.
GO Classes
asked
in
Linear Algebra
Mar 29, 2023
by
GO Classes
1.3k
views
goclasses2024_wq6
goclasses
linear-algebra
system-of-equations
multiple-selects
2-marks
21
votes
1
answer
162
GO Classes Weekly Quiz 6 | Linear Algebra | Question: 24
Let $A$ be a $3 \times 3$ matrix. Suppose that $A$ has eigenvalues $2$ and $-1,$ and suppose that $\mathbf{u}$ and $\mathbf{v}$ are eigenvectors corresponding to $2$ and $-1,$ ... ${\left[\begin{array}{c} 92 \\ -2 \\ 96 \end{array}\right]} $
GO Classes
asked
in
Linear Algebra
Mar 29, 2023
by
GO Classes
783
views
goclasses2024_wq6
goclasses
linear-algebra
eigen-vector
2-marks
15
votes
3
answers
163
GO Classes Weekly Quiz 6 | Linear Algebra | Question: 25
Let $u \in \mathbb{R}^n$ be such that $u^T u=1$ and set $A=u u^T$. What will be the sum of all eigenvalues of $A?$
GO Classes
asked
in
Linear Algebra
Mar 29, 2023
by
GO Classes
871
views
goclasses2024_wq6
numerical-answers
goclasses
linear-algebra
eigen-value
2-marks
13
votes
3
answers
164
GO Classes Weekly Quiz 6 | Linear Algebra | Question: 26
Given a matrix $A\left(m \times n\right)$ and $A x=b$. Consider below statements : $\text{S}: m<n$ $\mathrm{P}:\; A$ has $m \;\mathrm{Linearly ~Independent}$ columns $\text{R}:$ There is a solution for every $b$ ... $\text{R} \rightarrow \text{P}$ $\text{S} \rightarrow \sim \text{P}$ $(S$ and $\text{P}) \rightarrow \text{R}$
GO Classes
asked
in
Linear Algebra
Mar 29, 2023
by
GO Classes
919
views
goclasses2024_wq6
goclasses
linear-algebra
system-of-equations
multiple-selects
2-marks
18
votes
1
answer
165
GO Classes Weekly Quiz 6 | Linear Algebra | Question: 27
Consider the following set of (column) vectors: $X=\left\{\left[\begin{array}{l}x_1 \\ x_2 \\ x_3\end{array}\right] \in \mathbb{R}^3 \mid 2 x_1+3 x_2-x_3=0\right\}.$ Which of the following statements are true? Every element of ... Choose the correct option. Only I is true. Only II is true. Both I and II are true. Neither I, nor II are true.
GO Classes
asked
in
Linear Algebra
Mar 29, 2023
by
GO Classes
532
views
goclasses2024_wq6
goclasses
linear-algebra
vector-space
2-marks
11
votes
1
answer
166
GO Classes Weekly Quiz 6 | Linear Algebra | Question: 28
Choose the correct statements. If $b>\frac{2}{3}$, then $A=\left[\begin{array}{ll}2 & b \\ 3 & 1\end{array}\right]$ is invertible. If $P$ is an invertible matrix such that $B=P^{-1} A P,$ ... $m$ equations and $n$ variables, such that $m=n,$ always has a solution.
GO Classes
asked
in
Linear Algebra
Mar 29, 2023
by
GO Classes
552
views
goclasses2024_wq6
goclasses
linear-algebra
system-of-equations
multiple-selects
2-marks
4
votes
2
answers
167
GO Classes Weekly Quiz 6 | Linear Algebra | Question: 29
Given matrix $A\left(m \times n\right)$ such that $A x=b.$ Consider below statements : $\text{S1}:$ If $b$ is Linearly Dependent on cols of matrix, then it need not always have a unique solution. $\text{S2}:$ If columns of matrix are Linearly ... $\text{S1}$ is true and $\text{S2}$ is false $\mathrm{S} 2$ is true and $\mathrm{S} 1$ is false
GO Classes
asked
in
Linear Algebra
Mar 29, 2023
by
GO Classes
641
views
goclasses2024_wq6
goclasses
linear-algebra
system-of-equations
2-marks
19
votes
2
answers
168
GO Classes Weekly Quiz 6 | Linear Algebra | Question: 30
There exist a $3 \times 3$ real symmetric matrix $\text{S}$ ... $2$ is false Statement $1$ is false but Statement $2$ is true Both Statements are true Both Statements are false
GO Classes
asked
in
Linear Algebra
Mar 29, 2023
by
GO Classes
1.0k
views
goclasses2024_wq6
goclasses
linear-algebra
matrix
2-marks
0
votes
1
answer
169
#Eigen Vectors
Find the eigen values and eigen vector of the following matrix????
Çșȇ ʛấẗẻ
asked
in
Mathematical Logic
Mar 21, 2023
by
Çșȇ ʛấẗẻ
1.2k
views
eigen-value
linear-algebra
engineering-mathematics
matrix
Page:
« prev
1
2
3
4
5
6
7
8
9
10
11
...
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
(25)
Non GATE
(1.4k)
Others
(2.7k)
Admissions
(683)
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
79.7k
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