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

1 votes

1 answer

GO Classes CS/DA 2025 | Weekly Quiz 5 | Linear Algebra | Question: 15
Consider the following two statements: $S 1$. If $A B=I$, then $A$ is invertible. $S 2$. If $A$ is a $3 \times 3$ matrix and the equation $A \vec{x}=\left[\begin{array}{l}1 \\ 0 \\ 0\end{array}\right]$ has a unique ... $S 2$ is false $\mathrm{S} 1$ is false but $\mathrm{S} 2$ is true Both are true Both are false

Consider the following two statements:$S 1$. If $A B=I$, then $A$ is invertible.$S 2$. If $A$ is a $3 \times 3$ matrix and the equation $A \vec{x}=\left[\begin{array}{l}1...

GO Classes

102 views

GO Classes asked Apr 3

3 votes

2 answers

#linear algebra
why Eigen Vectors can not be zero ?

why Eigen Vectors can not be zero ?

srijankarak_123

141 views

srijankarak_123 asked Mar 23

0 votes

1 answer

#GATE
Is Vector Subspace, Span, Basis, Dimension part of the gate CSE engineering mathematics linear algebra syllabus ?

Is Vector Subspace, Span, Basis, Dimension part of the gate CSE engineering mathematics linear algebra syllabus ?

sup739

180 views

sup739 asked Feb 18

6 votes

2 answers

GATE CSE 2024 | Set 2 | Question: 37
Let $A$ be an $n \times n$ matrix over the set of all real numbers $\mathbb{R}$. Let $B$ be a matrix obtained from $A$ by swapping two rows. Which of the following statements is/are TRUE? The determinant of $B$ is the negative of the ... If $A$ is symmetric, then $B$ is also symmetric If the trace of $A$ is zero, then the trace of $B$ is also zero

Let $A$ be an $n \times n$ matrix over the set of all real numbers $\mathbb{R}$. Let $B$ be a matrix obtained from $A$ by swapping two rows. Which of the f...

Arjun

2.2k views

Arjun asked Feb 16

5 votes

8 answers

GATE CSE 2024 | Set 1 | Question: 2
The product of all eigenvalues of the matrix $\left[\begin{array}{lll}1 & 2 & 3 \\ 4 & 5 & 6 \\ 7 & 8 & 9\end{array}\right]$ is $-1$ $0$ $1$ $2$

The product of all eigenvalues of the matrix $\left[\begin{array}{lll}1 & 2 & 3 \\ 4 & 5 & 6 \\ 7 & 8 & 9\end{array}\right]$ is$-1$$0$$1$$2$

Arjun

2.9k views

Arjun asked Feb 16

12 votes

3 answers

GATE CSE 2024 | Set 1 | Question: 39
Let $A$ be any $n \times m$ matrix, where $m>n$. Which of the following statements is/are TRUE about the system of linear equations $Ax=0$? There exist at least $m-n$ linearly independent solutions to this system There exist $m-n$ ... solution in which at least $m-n$ variables are $0$ There exists a solution in which at least $n$ variables are non-zero

Let $A$ be any $n \times m$ matrix, where $m>n$. Which of the following statements is/are TRUE about the system of linear equations $Ax=0$?There exist at least $m-n...

Arjun

3.2k views

Arjun asked Feb 16

5 votes

1 answer

GO Classes Test Series 2024 | Mock GATE | Test 14 | Question: 22
Let $A$ be a $20 \times 11$ matrix with real entries. After performing some row operations on $A$, we get a matrix $B$ which has 12 nonzero rows. Which of the following is/are always true? The rank of $A$ is 12. The ranks of $A$ and $B$ are ... . If $v$ is a vector such that $A v=0$ then $B v$ is also 0. The rank of $B$ is at most 11.

Let $A$ be a $20 \times 11$ matrix with real entries. After performing some row operations on $A$, we get a matrix $B$ which has 12 nonzero rows. Which of the following i...

GO Classes

381 views

GO Classes asked Feb 5

7 votes

2 answers

GO Classes Test Series 2024 | Mock GATE | Test 14 | Question: 49
Consider a $2 \times 2$ matrix M. Which of the following are NOT POSSIBLE for the system of equations $M x=p?$ no solutions for some but not all $\vec{p}$; exactly one solution for all other $\vec{p}$ exactly one solution for ... some $\vec{p}$, exactly one solution for some $\vec{p}$ and more than one solution for some $\vec{p}$

Consider a $2 \times 2$ matrix M. Which of the following are NOT POSSIBLE for the system of equations $M x=p?$no solutions for some but not all $\vec{p}$; exactly one sol...

GO Classes

558 views

GO Classes asked Feb 5

2 votes

2 answers

Memory Based GATE DA 2024 | Question: 4
Consider the matrix \[ \mathrm{M} = \begin{bmatrix} 1 & 2 & 3 \\ 3 & 1 & 3 \\ 4 & 3 & 6 \end{bmatrix} \] Find the value of $|\mathrm{M}^2 + 12M|$.

Consider the matrix\[\mathrm{M} = \begin{bmatrix}1 & 2 & 3 \\3 & 1 & 3 \\4 & 3 & 6\end{bmatrix}\]Find the value of $|\mathrm{M}^2 + 12M|$.

GO Classes

536 views

GO Classes asked Feb 4

0 votes

0 answers

Memory Based GATE DA 2024 | Question: 5
Consider a matrix $M \in \mathbb{R}^{3 \times 3}$ and let $U$ be a 2-dimensional subspace such that $M$ is a projection onto $U$. Which of the following statements are true? $M^3 = M$ $M^2 = M$ The nullspace of $M$ is 1-dimensional. The nullspace of $M$ is 2-dimensional.

Consider a matrix $M \in \mathbb{R}^{3 \times 3}$ and let $U$ be a 2-dimensional subspace such that $M$ is a projection onto $U$. Which of the following statement...

GO Classes

228 views

GO Classes asked Feb 4

0 votes

2 answers

Memory Based GATE DA 2024 | Question: 6
Consider the matrix \[ \begin{bmatrix} 2 & -1 \\ 3 & 1 \end{bmatrix} \] What is the nature of the eigenvalues of the given matrix? Both eigenvalues are positive. One eigenvalue is negative. Eigenvalues are complex conjugate pairs. None of the above.

Consider the matrix\[\begin{bmatrix}2 & -1 \\3 & 1\end{bmatrix}\]What is the nature of the eigenvalues of the given matrix?Both eigenvalues are positive.One eigenvalue ...

GO Classes

270 views

GO Classes asked Feb 4

0 votes

1 answer

Memory Based GATE DA 2024 | Question: 29
Consider the vector $ u = \begin{bmatrix} 1 \\ 2 \\ 3 \\ 4 \\ 5 \end{bmatrix} $, and let $ M = uu^{\top} $. If $ \sigma_1, \sigma_2, \sigma_3, \ldots, \sigma_5 $ are the singular values of $ M $, what is the value of $ \sum_{i=1}^5 \sigma_i $?

Consider the vector $ u = \begin{bmatrix} 1 \\ 2 \\ 3 \\ 4 \\ 5 \end{bmatrix} $, and let $ M = uu^{\top} $. If $ \sigma_1, \sigma_2, \sigma_3, \ldots, \sigma_5 $ ar...

GO Classes

205 views

GO Classes asked Feb 4

0 votes

1 answer

Memory Based GATE DA 2024 | Question: 53
Consider the following scenarios involving linear algebra: For a $3 \times 3$ matrix, if some vector p has a unique solution, can there exist another vector q with an infinite solution? For a $3 \times 3$ matrix, if some vector p ... 2 \times 3\) matrix, if some vector p has a unique solution, can there exist another vector q with an infinite solution?

Consider the following scenarios involving linear algebra:For a $3 \times 3$ matrix, if some vector p has a unique solution, can there exist another vector q with an in...

GO Classes

143 views

GO Classes asked Feb 4

0 votes

0 answers

Memory Based GATE DA 2024 | Question: 60
Linear Algebra Question: Four options were given related to subspace R3. Something like this : A. $ \alpha \cdot x + \beta \cdot y $ B. $ \alpha^2 \cdot x + \beta^2 \cdot y $ C. $f(x) = 4x_1 + 2x_3 + 3x_3 $ D.

Linear Algebra Question: Four options were given related to subspace R3.Something like this :A. $ \alpha \cdot x + \beta \cdot y $B. \( \alpha^2 \cdot x + \beta^2 \cdot...

GO Classes

139 views

GO Classes asked Feb 4

7 votes

1 answer

GO Classes Test Series 2024 | Mock GATE | Test 13 | Question: 13
If $A$ is a $3 \times 3$ matrix such that $A\left(\begin{array}{l}0 \\ 1 \\ 2\end{array}\right)=\left(\begin{array}{l}1 \\ 0 \\ 0\end{array}\right)$ ... $\left(\begin{array}{r}1 \\ -1 \\ 0\end{array}\right)$ $\left(\begin{array}{r}9 \\ 10 \\ 11\end{array}\right)$

If $A$ is a $3 \times 3$ matrix such that $A\left(\begin{array}{l}0 \\ 1 \\ 2\end{array}\right)=\left(\begin{array}{l}1 \\ 0 \\ 0\end{array}\right)$ and $A\left(\begin{ar...

GO Classes

582 views

GO Classes asked Jan 28

9 votes

2 answers

GO Classes Test Series 2024 | Mock GATE | Test 13 | Question: 43
Let $A$ be a $2 \times 2$ matrix for which there is a constant $k$ such that the sum of the entries in each row and each column is $k$. Which of the following must be an eigenvector of $A?$ ... $\left[\begin{array}{l}1 \\ 1\end{array}\right]$. I only II only III only I and II only

Let $A$ be a $2 \times 2$ matrix for which there is a constant $k$ such that the sum of the entries in each row and each column is $k$. Which of the following must be an ...

GO Classes

509 views

GO Classes asked Jan 28

7 votes

2 answers

GO Classes Test Series 2024 | Mock GATE | Test 12 | Question: 7
Let $\text{A}$ be a $20 \times 11$ matrix with real entries. After performing some row operations on $\text{A}$, we get a matrix $\text{B}$ which has $12$ nonzero rows. Which of the following is/are always true? The rank of $\text{A}$ ... that $\text{A} v=0$ then $\text{B} v$ is also $0.$ The rank of $\text{B}$ is at most $11.$

Let $\text{A}$ be a $20 \times 11$ matrix with real entries. After performing some row operations on $\text{A}$, we get a matrix $\text{B}$ which has $12$ nonzero rows. W...

GO Classes

635 views

GO Classes asked Jan 21

4 votes

1 answer

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 $A?$

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...

GO Classes

774 views

GO Classes asked Jan 13

5 votes

1 answer

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 $m \times 1, m \times n$ ... $\operatorname{rank}[A]>$ $\operatorname{rank}[A \mid b]$.

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 ...

GO Classes

515 views

GO Classes asked Jan 13

0 votes

0 answers

Linear Transformation of Matrix

Debargha Mitra Roy

68 views

Debargha Mitra Roy asked Jan 12

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