Search results for matrix / GATE Overflow for GATE CSE

79 votes

7 answers

1

GATE CSE 2018 | Question: 26
Consider a matrix P whose only eigenvectors are the multiples of $\begin{bmatrix} 1 \\ 4 \end{bmatrix}$. Consider the following statements. P does not have an inverse P has a repeated eigenvalue P cannot be diagonalized Which one of the ... III are necessarily true Only II is necessarily true Only I and II are necessarily true Only II and III are necessarily true

Consider a matrix P whose only eigenvectors are the multiples of $\begin{bmatrix} 1 \\ 4 \end{bmatrix}$.Consider the following statements.P does not have an inverseP has ...

gatecse

27.4k views

gatecse asked Feb 14, 2018

45 votes

14 answers

2

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 __________

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...

Arjun

18.6k views

Arjun asked Feb 18, 2021

18 votes

5 answers

3

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 __________.

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 __...

Arjun

15.6k views

Arjun asked Feb 18, 2021

19 votes

4 answers

4

GATE CSE 2022 | Question: 10
Consider the following two statements with respect to the matrices $\textit{A}_{m \times n}, \textit{B}_{n \times m}, \textit{C}_{n \times n}$ and $ \textit{D}_{n \times n}.$ Statement $1: tr \text{(AB)} = tr \text{(BA)}$ ... $2$ is correct. Both Statement $1$ and Statement $2$ are correct. Both Statement $1$ and Statement $2$ are wrong.

Consider the following two statements with respect to the matrices $\textit{A}_{m \times n}, \textit{B}_{n \times m}, \textit{C}_{n \times n}$ and $ \textit{D}_{n \times ...

Arjun

10.8k views

Arjun asked Feb 15, 2022

42 votes

7 answers

5

GATE CSE 2016 Set 2 | Question: 38
Let $A_{1}, A_{2}, A_{3}$ and $A_{4}$ be four matrices of dimensions $10 \times 5, 5 \times 20, 20 \times 10$ and $10 \times 5$, respectively. The minimum number of scalar multiplications required to find the product $A_{1}A_{2}A_{3}A_{4}$ using the basic matrix multiplication method is _________.

Let $A_{1}, A_{2}, A_{3}$ and $A_{4}$ be four matrices of dimensions $10 \times 5, 5 \times 20, 20 \times 10$ and $10 \times 5$, respectively. The minimum number of scala...

Akash Kanase

22.7k views

Akash Kanase asked Feb 12, 2016

22 votes

5 answers

6

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 $\textit{U}$ ... $\textit{L}_{32}= - \frac{1}{2}, \textit{U}_{33}= - \frac{1}{2}, x_{1}= 0$

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} +...

Arjun

11.3k views

Arjun asked Feb 15, 2022

15 votes

3 answers

7

GATE CSE 2020 | Question: 27
Let $A$ and $B$ be two $n \times n$ matrices over real numbers. Let rank($M$) and $\text{det}(M)$ denote the rank and determinant of a matrix $M$, respectively. Consider the following statements. $\text{rank}(AB) = \text{rank }(A) \text{rank }(B)$ ... Which of the above statements are TRUE? I and II only I and IV only II and III only III and IV only

Let $A$ and $B$ be two $n \times n$ matrices over real numbers. Let rank($M$) and $\text{det}(M)$ denote the rank and determinant of a matrix $M$, respectively. Consider...

Arjun

10.1k views

Arjun asked Feb 12, 2020

25 votes

7 answers

8

GATE CSE 2004 | Question: 26
The number of different $n \times n $ symmetric matrices with each element being either 0 or 1 is: (Note: $\text{power} \left(2, X\right)$ is same as $2^X$) $\text{power} \left(2, n\right)$ $\text{power} \left(2, n^2\right)$ $\text{power} \left(2,\frac{ \left(n^2+ n \right) }{2}\right)$ $\text{power} \left(2, \frac{\left(n^2 - n\right)}{2}\right)$

The number of different $n \times n $ symmetric matrices with each element being either 0 or 1 is: (Note: $\text{power} \left(2, X\right)$ is same as $2^X$)$\text{power} ...

Kathleen

12.6k views

Kathleen asked Sep 18, 2014

38 votes

7 answers

9

GATE IT 2008 | Question: 29
If $M$ is a square matrix with a zero determinant, which of the following assertion (s) is (are) correct? S1: Each row of $M$ can be represented as a linear combination of the other rows S2: Each column of $M$ can be represented as a linear combination of the other columns S3 ... solution S4: $M$ has an inverse $S3$ and $S2$ $S1$ and $S4$ $S1$ and $S3$ $S1, S2$ and $S3$

If $M$ is a square matrix with a zero determinant, which of the following assertion (s) is (are) correct?S1: Each row of $M$ can be represented as a linear combination of...

Ishrat Jahan

9.6k views

Ishrat Jahan asked Oct 28, 2014

7 votes

2 answers

10

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

624 views

GO Classes asked Jan 21

7 votes

1 answer

11

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

577 views

GO Classes asked Jan 28

5 votes

1 answer

12

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

375 views

GO Classes asked Feb 5

0 votes

0 answers

13

Linear Transformation of Matrix

Debargha Mitra Roy

67 views

Debargha Mitra Roy asked Jan 12

0 votes

1 answer

14

ISRO 2024
The complexity of matrix multiplication of two matrices A and B whose orders are $m \times n$ and $n \times p$ respectively is $\text{O(m} \times p)$ $\text{O(m} \times n^2 \times p)$ $\text{O(m} \times n \times p^2)$ $\text{O(m} \times n \times p)$

The complexity of matrix multiplication of two matrices A and B whose orders are $m \times n$ and $n \times p$ respectively is$\text{O(m} \times p)$$\text{O(m} \times n^2...

Ramayya

236 views

Ramayya asked Jan 7

0 votes

0 answers

15

Diagonalization of Matrix

Debargha Mitra Roy

60 views

Debargha Mitra Roy asked Jan 11

0 votes

0 answers

16

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 = $ ______

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 di...

Debargha Mitra Roy

102 views

Debargha Mitra Roy asked Jan 11

0 votes

0 answers

17

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.

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{bm...

rajveer43

76 views

rajveer43 asked Jan 10

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