Syllabus: Matrices, determinants, System of linear equations, Eigenvalues and eigenvectors, LU decomposition.

$$\scriptsize{\overset{{\large{\textbf{Mark Distribution in Previous GATE}}}}{\begin{array}{|c|c|c|c|c|c|c|c|}\hline
\textbf{Year}& \textbf{2022} & \textbf{2021-1}&\textbf{2021-2}&\textbf{2020}&\textbf{2019}&\textbf{2018}&\textbf{2017-1}&\textbf{2017-2}&\textbf{2016-1}&\textbf{2016-2}&\textbf{Minimum}&\textbf{Average}&\textbf{Maximum}
\\\hline\textbf{1 Mark Count} & 1 &0&1&0&1&1&1&1&1&2&0&0.9&2
\\\hline\textbf{2 Marks Count} & 2 &1&1&1&1&1&2&1&0&0&0&1&2
\\\hline\textbf{Total Marks} & 5 &2&3&2&3&3&5&3&1&2&\bf{1}&\bf{2.9}&\bf{5}\\\hline
\end{array}}}$$

Recent questions in Linear Algebra

12 votes

2 answers

151

GO Classes CS/DA 2025 | Weekly Quiz 3 | Fundamental Course and Linear Algebra | Question: 6
Consider a set of $n$ linearly independent vectors $\left\{\vec{w}_1, \ldots, \vec{w}_n\right\} \in \mathbb{R}^n$. A vector $\vec{u} \in \mathbb{R}^n$ will: Option $1.$ Always be a linear ... $2$ is correct then enter $\text{ 2 }.$

Consider a set of $n$ linearly independent vectors $\left\{\vec{w}_1, \ldots, \vec{w}_n\right\} \in \mathbb{R}^n$. A vector $\vec{u} \in \mathbb{R}^n$ will:Option $1.$ Al...

GO Classes

759 views

GO Classes asked Mar 14, 2023

9 votes

3 answers

152

GO Classes CS/DA 2025 | Weekly Quiz 3 | Fundamental Course and Linear Algebra | Question: 7
Which of the following set is/are linearly independent? $\left\{\left[\begin{array}{l}1 \\ 2\end{array}\right],\left[\begin{array}{l}2 \\ 1\end{array}\right]\right\}$ ...

Which of the following set is/are linearly independent?$\left\{\left[\begin{array}{l}1 \\ 2\end{array}\right],\left[\begin{array}{l}2 \\ 1\end{array}\right]\right\}$ $\le...

GO Classes

765 views

GO Classes asked Mar 14, 2023

11 votes

7 answers

153

GO Classes CS/DA 2025 | Weekly Quiz 3 | Fundamental Course and Linear Algebra | Question: 8
$a\left[\begin{array}{l}1 \\ 2 \\ 3 \\ 4 \\ 5\end{array}\right]+b\left[\begin{array}{c}-1 \\ 2 \\ -3 \\ 4 \\ -5\end{array}\right]=\left[\begin{array}{l}0 \\ 0 \\ 0 \\ 0 \\ 0\end{array}\right]$ How many number of pairs $(a, b)$ are there, that satisfy the above equation? $0$ $1$ Infinite $2$

$$a\left[\begin{array}{l}1 \\ 2 \\ 3 \\ 4 \\ 5\end{array}\right]+b\left[\begin{array}{c}-1 \\ 2 \\ -3 \\ 4 \\ -5\end{array}\right]=\left[\begin{array}{l}0 \\ 0 \\ 0 \\ 0 ...

GO Classes

638 views

GO Classes asked Mar 14, 2023

9 votes

4 answers

154

GO Classes CS/DA 2025 | Weekly Quiz 3 | Fundamental Course and Linear Algebra | Question: 9
Given a set of vectors $\text{S}(|\text{S}| \geq n)$, with all vectors in $\mathbb{R}^n$, which of the following is a necessary and sufficient condition for the vectors of $\text{S}$ to be Linearly ... $u$ can be represented as a linear combination of vectors (other than $u$ ) of the set $\text{S}$.

Given a set of vectors $\text{S}(|\text{S}| \geq n)$, with all vectors in $\mathbb{R}^n$, which of the following is a necessary and sufficient condition for the vectors o...

GO Classes

746 views

GO Classes asked Mar 14, 2023

20 votes

6 answers

155

GO Classes CS/DA 2025 | Weekly Quiz 3 | Fundamental Course and Linear Algebra | Question: 10
Which of the following is(are) sufficient argument(s) to show that the vectors of set $\text{S}$ ... $7 u+(-1) v+1 w=\left[\begin{array}{l}0 \\ 0 \\ 0\end{array}\right]$

Which of the following is(are) sufficient argument(s) to show that the vectors of set $\text{S}$ are linearly dependent?$$\text{S}=\left\{u=\left[\begin{array}{c}1 \\-2 \...

GO Classes

1.4k views

GO Classes asked Mar 14, 2023

16 votes

5 answers

156

GO Classes CS/DA 2025 | Weekly Quiz 3 | Fundamental Course and Linear Algebra | Question: 11
Which of the following is(are) true for the following system of linear equations $\text{AX}=\overrightarrow{0}$ ... $\text{AX}=\overrightarrow{0}$.

Which of the following is(are) true for the following system of linear equations $\text{AX}=\overrightarrow{0}$$$\left[\begin{array}{ccc}2 & 3 & -5 \\-5 & -1 & 32 \\2 & -...

GO Classes

1.1k views

GO Classes asked Mar 14, 2023

8 votes

3 answers

157

GO Classes CS/DA 2025 | Weekly Quiz 3 | Fundamental Course and Linear Algebra | Question: 12
Given a set $\text{S}$ of vectors in $\mathbb{R}^n$, and set $\text{X(X} \subset \text{S})$ and $\text{Y(S} \subset \text{Y}),$ mark all the statements which are always true: If the ... . If the vectors of $\text{S}$ are Linearly Independent, then the vectors of $\text{Y}$ are also Linearly Independent.

Given a set $\text{S}$ of vectors in $\mathbb{R}^n$, and set $\text{X(X} \subset \text{S})$ and $\text{Y(S} \subset \text{Y}),$ mark all the statements which are always t...

GO Classes

588 views

GO Classes asked Mar 14, 2023

9 votes

2 answers

158

GO Classes CS/DA 2025 | Weekly Quiz 3 | Fundamental Course and Linear Algebra | Question: 14
Which of the following is/are CORRECT? $u,v, \text{ and } w$ are vectors in $\mathbb{R}^n$. A set $\{u, v, w\}$ is linearly independent if $ u $ can not be written as linear combination of $v$ ... $\{\mathbf{u}, \mathbf{v}, \mathbf{w}\}$ is linearly independent.

Which of the following is/are CORRECT?$u,v, \text{ and } w$ are vectors in $\mathbb{R}^n$.A set $\{u, v, w\}$ is linearly independent if $ u $ can not be written as linea...

GO Classes

720 views

GO Classes asked Mar 14, 2023

18 votes

2 answers

159

GO Classes CS/DA 2025 | Weekly Quiz 3 | Fundamental Course and Linear Algebra | Question: 15
$\mathrm{S} 1:$ A set of two vectors in $\mathbb{R}^n$ is Linealy dependent if at least one vector is a multiple of the other. $\text{S2}:$ A set of $n$ vectors in $\mathbb{R}^n$ is Linealy independent if and ... $\text{S} 1$ is incorrect $\text{S} 1$ and $\text{S} 2$ both are incorrect

$\mathrm{S} 1:$ A set of two vectors in $\mathbb{R}^n$ is Linealy dependent if at least one vector is a multiple of the other.$\text{S2}:$ A set of $n$ vectors in $\mathb...

GO Classes

964 views

GO Classes asked Mar 14, 2023

4 votes

2 answers

160

TIFR CSE 2023 | Part B | Question: 5
Consider unit vectors $\mathbf{a}$ and $\mathbf{b}$ in $\mathbb{R}^{n}$. Let $\mathbf{w}$ be an arbitrary vector in $\mathbb{R}^{n}$ and $\eta$ be a positive real number such that \[ \mathbf{a}^{\mathbf{T}} \mathbf{b} \geq \eta>0 \geq \ ... $\text{(S3)}$ must be true, but statement $\text{(S2)}$ may be false. Statement $\text{(S1)}$ may be false.

Consider unit vectors $\mathbf{a}$ and $\mathbf{b}$ in $\mathbb{R}^{n}$. Let $\mathbf{w}$ be an arbitrary vector in $\mathbb{R}^{n}$ and $\eta$ be a positive real number ...

admin

384 views

admin asked Mar 14, 2023

4 votes

0 answers

161

TIFR CSE 2023 | Part A | Question: 1
Let $A$ be a symmetric $3 \times 3$ matrix with real entries. Let $u$ and $v$ be non-zero vectors with real entries such that $A u=2 u$ and $A v=3 v$. From the set of values $\{0,1,-1\}$, which values can the inner product $u^{T} v$ take? $0$ only $1$ only $-1$ only All of the values $0,1$ and $-1$ None of the values $0,1$ and $-1$

Let $A$ be a symmetric $3 \times 3$ matrix with real entries. Let $u$ and $v$ be non-zero vectors with real entries such that $A u=2 u$ and $A v=3 v$. From the set of val...

admin

539 views

admin asked Mar 14, 2023

4 votes

1 answer

162

TIFR CSE 2023 | Part A | Question: 3
$A$ is an $n \times n$ matrix with real-valued entries. Further, there exists a vector $x \neq 0$ such that $A x=0$. Now consider a given vector $b$ in $\mathbb{R}^{n}$. How many possible vectors $z$ exist, so that $A z=b?$ $0$ $1$ $n-1$ $n$ Either $0$ or infinite

$A$ is an $n \times n$ matrix with real-valued entries. Further, there exists a vector $x \neq 0$ such that $A x=0$. Now consider a given vector $b$ in $\mathbb{R}^{n}$. ...

admin

451 views

admin asked Mar 14, 2023

3 votes

1 answer

163

TIFR CSE 2023 | Part A | Question: 5
Suppose $A$ is a $2 \times 2$ matrix such that the sum of the principal diagonal entries of $A$ is $10$ and the sum of the principal diagonal entries of $A^{2}$ is $20$. (For any $2 \times 2$ matrix $B$, the ... $80$ Nonzero, but cannot be uniquely determined from the above data. Cannot be uniquely determined from the above data, and could also be zero.

Suppose $A$ is a $2 \times 2$ matrix such that the sum of the principal diagonal entries of $A$ is $10$ and the sum of the principal diagonal entries of $A^{2}$ is $20$. ...

admin

337 views

admin asked Mar 14, 2023

4 votes

1 answer

164

TIFR CSE 2023 | Part A | Question: 15
Consider the $n \times n$ matrix $M$ ... $S$ have? $1$ $\left(\begin{array}{l}n \\ 2\end{array}\right)$ $n$ ! $(n !)^{2}$ $n$

Consider the $n \times n$ matrix $M$ defined as follows:$$M=\left(\begin{array}{cccc}1 & 2 & \ldots & n \\n+1 & n+2 & \ldots & 2 n \\2 n+1 & 2 n+2 & \ldots & 3 n \\\vdots...

admin

542 views

admin asked Mar 14, 2023

0 votes

0 answers

165

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

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{ma...

kidussss

387 views

kidussss asked Mar 7, 2023

0 votes

0 answers

166

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

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_{...

kidussss

245 views

kidussss asked Mar 7, 2023

21 votes

4 answers

167

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 & ... $\operatorname{det}(B)=-\operatorname{det}(A)$ $\operatorname{det}(A)=0$ $\operatorname{det}(A B)=\operatorname{det}(A)+\operatorname{det}(B)$

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 & 1 & 2 \\4 & 1 & 2...

admin

11.4k views

admin asked Feb 15, 2023

9 votes

4 answers

168

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 $\lambda_{1}+\lambda_{2}+\lambda_{3}+\lambda_{4}+\lambda_{5}=$____________

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 eigenva...

admin

13.2k views

admin asked Feb 15, 2023

4 votes

2 answers

169

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] $ ... $\operatorname{det} \mathrm{B}=-\operatorname{det} \mathrm{A}$ $\operatorname{det} \mathrm{A}=\operatorname{det} \mathrm{B}$

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 & 1 & 2 \\4 & 1 & 2...

GO Classes

2.5k views

GO Classes asked Feb 5, 2023

0 votes

0 answers

170

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.

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

311 views

kidussss asked Jan 13, 2023

Page:

« prev
1
...
3
4
5
6
7
8
9
10
11
12
13
...
58
next »

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