Recent questions tagged matrices

0 votes

1 answer

1

Simple Determinant
how to prove determinant 1 and 2 are same by some row-column manipulation ,please Help??

asked 1 day ago in Linear Algebra by BHASHKAR (21 points) | 12 views

+1 vote

0 answers

2

#set theory #groups
Consider the set H of all 3 × 3 matrices of the type: $\begin{bmatrix} a&f&e\\ 0&b&d\\ 0&0&c\\ \end{bmatrix}$ where a, b, c, d, e and f are real numbers and $abc ≠ 0$. Under the matrix multiplication operation, the set H is: (a) a group (b) a monoid but not a group (c) a semigroup but not a monoid (d) neither a group nor a semigroup

asked Jan 5 in Set Theory & Algebra by Kunal Kadian Active (2.4k points) | 43 views

0 votes

0 answers

3

Determinant
True and false IF A is 5*5 matrix then det(4$A^{3}$)=$4^{5}det(A^{3}))$ det($(4A)^{3}$)=$det(4^{3}A^{3}))$ i think both are true ??

asked Jan 4 in Mathematical Logic by Gurdeep Saini Loyal (7.7k points) | 19 views

+2 votes

1 answer

4

GATEBOOK-2019-LA-1-1
The characteristic roots of a $3 \times 3$ matrix $A$ are $2, 2, 8.$ The constant term in the characteristic polynomial is $12$ $18$ $32$ $128$

asked Dec 23, 2018 in Linear Algebra by GATEBOOK Boss (13.8k points) | 136 views

+1 vote

1 answer

5

Cases when LU decomposition is possible.
I had already visited below link but was unable to grasp it. https://math.stackexchange.com/questions/218770/when-does-a-square-matrix-have-an-lu-decomposition. I made some form of self-analysis, let me know if I am in the correct ... pivot, and if such cannot be fixed without a row shuffle operation, then LU decomposition is not possible. Am I correct?

asked Nov 18, 2018 in Linear Algebra by Ayush Upadhyaya Boss (23k points) | 94 views

0 votes

0 answers

6

GATE-ME-2016

asked Nov 6, 2018 in Linear Algebra by aditi19 Active (2.2k points) | 80 views

+3 votes

2 answers

7

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

asked Sep 20, 2018 in Linear Algebra by aditi19 Active (2.2k points) | 108 views

0 votes

0 answers

8

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

asked Aug 8, 2018 in Linear Algebra by pankaj_vir Boss (10k points) | 59 views

0 votes

2 answers

9

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, 2018 in Linear Algebra by pankaj_vir Boss (10k points) | 112 views

0 votes

1 answer

10

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, 2018 in Linear Algebra by ZeroFriction (15 points) | 131 views

0 votes

3 answers

11

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, 2018 in Linear Algebra by saumya mishra Active (1.5k points) | 159 views

+1 vote

1 answer

12

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, 2018 in Linear Algebra by srestha Veteran (106k points) | 130 views

+1 vote

3 answers

13

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, 2018 in Linear Algebra by srestha Veteran (106k points) | 344 views

0 votes

0 answers

14

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, 2018 in Linear Algebra by srestha Veteran (106k points) | 191 views

+4 votes

4 answers

15

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, 2018 in Linear Algebra by jjayantamahata Active (1.7k points) | 289 views

+1 vote

2 answers

16

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, 2018 in Mathematical Logic by jjayantamahata Active (1.7k points) | 165 views

+1 vote

2 answers

17

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, 2018 in Mathematical Logic by jjayantamahata Active (1.7k points) | 126 views

+3 votes

3 answers

18

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, 2018 in Linear Algebra by jjayantamahata Active (1.7k points) | 223 views

+3 votes

1 answer

19

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, 2018 in Linear Algebra by Avik Chowdhury Junior (891 points) | 228 views

+3 votes

1 answer

20

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, 2018 in Linear Algebra by Avik Chowdhury Junior (891 points) | 116 views

+1 vote

1 answer

21

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, 2018 in Linear Algebra by Avik Chowdhury Junior (891 points) | 261 views

+2 votes

2 answers

22

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, 2018 in Linear Algebra by Avik Chowdhury Junior (891 points) | 141 views

+1 vote

2 answers

23

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, 2018 in Linear Algebra by Avik Chowdhury Junior (891 points) | 518 views

+2 votes

2 answers

24

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, 2018 in Linear Algebra by Avik Chowdhury Junior (891 points) | 1.9k views

+1 vote

1 answer

25

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, 2018 in Linear Algebra by Avik Chowdhury Junior (891 points) | 222 views

0 votes

2 answers

26

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, 2018 in Mathematical Logic by jjayantamahata Active (1.7k points) | 68 views

+1 vote

1 answer

27

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, 2018 in Linear Algebra by srestha Veteran (106k points) | 120 views

+1 vote

1 answer

28

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, 2018 in Linear Algebra by Prince Sindhiya Loyal (6.1k points) | 130 views

0 votes

1 answer

29

GATE 2018 Maths - 22(Electronics and Communication Engineering)
Consider matrix $A =$ $\begin{bmatrix} k &2k \\ k^{2}-k &k^{2} \end{bmatrix}$ and $x =$ $\begin{bmatrix} x1\\x2 \end{bmatrix}$ The number of distinct real values of $k$ for which the equation $Ax = 0$ has infinitely many solutions is _______.

asked Feb 21, 2018 in Calculus by Lakshman Patel RJIT Boss (26.8k points) | 273 views

+1 vote

2 answers

30

GATE 2018 Maths - 29 (Chemical Engineering)
For the matrix $A = \begin{bmatrix}cos\theta & -sin\theta \\ sin\theta & cos\theta \end{bmatrix}$ if $\textit{det}$ stands for the determinant and $A^T$ is the transpose of $A$ then the value of $\textit{det}(A^TA)$ is __________ .

asked Feb 20, 2018 in Linear Algebra by Lakshman Patel RJIT Boss (26.8k points) | 131 views

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