Recent questions tagged matrices

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1 answer

1

Cases when LU decomposition is possible.

asked Nov 18 in Linear Algebra by Ayush Upadhyaya Boss (19k points) | 69 views

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0 answers

2

GATE-ME-2016

asked Nov 6 in Linear Algebra by aditi19 Active (2.1k points) | 54 views

+3 votes

2 answers

3

Eigen Value
An orthogonal matrix A has eigen values 1, 2 and 4. What is the trace of the matrix

asked Sep 20 in Linear Algebra by aditi19 Active (2.1k points) | 90 views

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0 answers

4

Invertible Matrix
Let $A$ be a nilpotent matrix. Show that $I + A$ is invertible.

asked Aug 8 in Linear Algebra by pankaj_vir Loyal (9.7k points) | 51 views

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2 answers

5

Invertible Matrix
Let A be a $5 × 5$ invertible matrix with row sums $1$. That is $\sum_{j=1}^{5} a_{ij} = 1$ for $1 \leq i\leq 5$. Then, what is the sum of all entries of $A^{-1}$.

asked Aug 8 in Linear Algebra by pankaj_vir Loyal (9.7k points) | 97 views

0 votes

1 answer

6

Inversion of a matrix - CSIR question
Let A be 3x3 matrix. Suppose 1 and -1 are two of the three Eigen Values of A and 18 is one of the Eigen Values of A2+3A. Then____ a.) Both A and A2+3A are invertible. b.) A2+3A but A is not. c.) A is invertible but A2+3A is not invertible. d.) Both A and A2+3A are not invertible.

asked Jul 5 in Linear Algebra by ZeroFriction (15 points) | 110 views

0 votes

3 answers

7

Made easy test
Consider the rank of matrix $'A'$ of size $(m \times n)$ is $"m-1"$. Then, which of the following is true? $AA^T$ will be invertible. $A$ have $"m-1"$ linearly independent rows and $"m-1"$ linearly ... $"n"$ linearly independent columns. $A$ will have $"m-1"$ linearly independent rows and $"n-1"$ independent columns.

asked May 31 in Linear Algebra by saumya mishra Active (1.5k points) | 144 views

+1 vote

1 answer

8

Matrix
Each row of M can be represented as a linear combination of the other rows 1)Does that mean linear combination of other rows will be 0? how ? 2)And also , is linear combination means add, subtract, multiply and divide , but not squaring or root or exponential operation,right? https://gateoverflow.in/3319/gate2008-it-29

asked May 30 in Linear Algebra by srestha Veteran (104k points) | 122 views

+1 vote

3 answers

9

Matrix
The matrix $A=\begin{bmatrix} 1 &4 \\ 2 &3 \end{bmatrix}$ satisfies the following polynomial $A^{5}-4A^{4}-7A^{3}+11A^{2}-2A+kI=0$ Then the value of k is ______________

asked May 26 in Linear Algebra by srestha Veteran (104k points) | 274 views

0 votes

0 answers

10

Matrix
To find the product of the non-zero eigenvalues of the matrix is ____ ... $\lambda =-1,2,0$ Where is my mistake, plz tell me

asked May 14 in Linear Algebra by srestha Veteran (104k points) | 186 views

+4 votes

4 answers

11

ISI-2017-29
Suppose the rank of the matrix $\begin{pmatrix}1&1&2&2\\1&1&1&3\\a&b&b&1\end{pmatrix}$ is $2$ for some real numbers $a$ and $b$. Then $b$ equals $1$ $3$ $1/2$ $1/3$

asked Mar 29 in Linear Algebra by jjayantamahata Active (1.6k points) | 268 views

+1 vote

2 answers

12

ISI-2017-19
If $\alpha, \beta$ and $\gamma$ are the roots of $x^3 - px +q = 0$, then the value of the determinant $\begin{vmatrix}\alpha & \beta & \gamma\\\beta & \gamma & \alpha\\\gamma & \alpha & \beta\end{vmatrix}$ is $p$ $p^2$ $0$ $p^2+6q$

asked Mar 28 in Mathematical Logic by jjayantamahata Active (1.6k points) | 161 views

+1 vote

2 answers

13

ISI-2017-15
The diagonal elements of a square matrix $M$ are odd integers while the off-diagonals are even integers. Then $M$ must be singular $M$ must be nonsingular There is not enough information to decide the singularity of $M$ $M$ must have a positive eigenvalue.

asked Mar 27 in Mathematical Logic by jjayantamahata Active (1.6k points) | 123 views

+3 votes

3 answers

14

ISI-2017-5
If $A$ is a $2 \times 2$ matrix such that trace $A = det \ A = 3,$ then what is the trace of $A^{-1}$? $1$ $\left(\dfrac{1}{3}\right)$ $\left(\dfrac{1}{6}\right)$ $\left(\dfrac{1}{2}\right)$

asked Mar 27 in Linear Algebra by jjayantamahata Active (1.6k points) | 198 views

+3 votes

1 answer

15

Made easy workbook
Let $A$ be a $4\times 4$ matrix with real entries such that $-1,1,2,-2$ are eigen values.If $B=A^4-5A^2+5I$ then trace of $A+B$ is...........

asked Mar 22 in Linear Algebra by Avik Chowdhury Junior (837 points) | 195 views

+3 votes

1 answer

16

Madeeasy workbook
The number of different matrices that can be formed with elements $0,1,2,3$; each matrix having $4$ elements is $2\times 4^4$ $3\times 4^4$ $4\times 4^4$ $3\times 2^4$

asked Mar 22 in Linear Algebra by Avik Chowdhury Junior (837 points) | 106 views

+1 vote

1 answer

17

Madeeasy workbook
Let $A$ be a $3\times 3$ matrix with Eigen values $-1,1,0$.Then $\mid A^{100}+I\mid$ is...

asked Mar 22 in Linear Algebra by Avik Chowdhury Junior (837 points) | 241 views

+2 votes

2 answers

18

Madeeasy workbook
A $3\times 3$ matrix $P$ is such that $P^3 =P$.Then the eigenvalues of $P$ are $1,1,1$ $1,0.5+j(0.886),0.5-j(0.866)$ $1,-0.5+j(0.866),-0.5-j(0.886)$ $0,1,-1$

asked Mar 22 in Linear Algebra by Avik Chowdhury Junior (837 points) | 129 views

+1 vote

2 answers

19

Madeeasy workbook
Let $A$ be a $3\times 3$ matrix such that $\mid A-I \mid=0$.If trace of $A=13$ and $det A = 32$ then sum of squares of the eigen values of $A$ is ..... $82$ $13$ $169$ $81$

asked Mar 22 in Linear Algebra by Avik Chowdhury Junior (837 points) | 417 views

+2 votes

2 answers

20

Madeeasy workbook
Let $A$ be a $3\times 4$ matrix.The system of equations $Ax=0$ has unique solution Infinite solution No solution Exactly 2 solutions

asked Mar 22 in Linear Algebra by Avik Chowdhury Junior (837 points) | 1.6k views

+1 vote

1 answer

21

Made easy workbook
Let $A = (a_{ij})_{n\times n}$ such that $a_{ij}=3$ for all $i,j$ then nullity of $A$ is $n-1$ $n-3$ $n$ $0$

asked Mar 22 in Linear Algebra by Avik Chowdhury Junior (837 points) | 179 views

0 votes

2 answers

22

ISI-2014-18
Let $D_1 = det \begin{pmatrix}a & b & c\\x &y & z\\p& q & r\end{pmatrix}$ and $D_2 = det \begin{pmatrix}-x & a & -p\\y &-b & q\\z & -c & r\end{pmatrix}$ Then $D_1 = D_2$ $D_1 = 2D_2$ $D_1 = -D_2$ $D_2 = 2D_1$

asked Mar 18 in Mathematical Logic by jjayantamahata Active (1.6k points) | 65 views

+1 vote

1 answer

23

Determinant
Find the determinant of the $n\times n$ ... $D_{n}-2cos\Theta D_{n-1}+D_{n-2}=0$? Plz explain

asked Mar 13 in Linear Algebra by srestha Veteran (104k points) | 114 views

+1 vote

1 answer

24

Eigen value of the following matrix
The eigen value of the following matrix is $\begin{bmatrix}1&1&1\\1&1&1\\1&1&1\end{bmatrix}$ $1, 1, 1$ $1, 0, 0$ $3, 0, 0$ $0, 0, 0$

asked Mar 3 in Linear Algebra by Prince Sindhiya Loyal (5.3k points) | 120 views

0 votes

1 answer

25

GATE 2018 Maths - 22(Electronics and Communication Engineering)

asked Feb 21 in Calculus by Lakshman Patel RJIT Boss (20.8k points) | 254 views

+1 vote

2 answers

26

GATE 2018 Maths - 29 (Chemical Engineering)

asked Feb 20 in Linear Algebra by Lakshman Patel RJIT Boss (20.8k points) | 120 views

+13 votes

3 answers

27

GATE2018-26
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 following options ... and III are necessarily true Only II is necessarily true Only I and II are necessarily true Only II and III are necessarily true

asked Feb 14 in Linear Algebra by gatecse Boss (18.3k points) | 2.9k views

0 votes

0 answers

28

Gate_2018_Model_Paper
How to solve it for M^-1?

asked Feb 1 in Mathematical Logic by Harikesh Kumar Active (1.4k points) | 79 views

0 votes

0 answers

29

Matrix

asked Jan 31 in Linear Algebra by srestha Veteran (104k points) | 104 views

+1 vote

1 answer

30

Test_series
If an idempotent matrix is also Skew-Symmetric then it must be a Null matrix an involuntary matrix an identity matrix Harmitian matrix

asked Jan 21 in Mathematical Logic by vijay_jr Active (1.1k points) | 176 views

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