Recent questions tagged matrices

0 votes

2 answers

1

GATE 2017:EC
Consider the $5\times 5$ matrix: $\begin{bmatrix} 1 & 2 &3 & 4 &5 \\ 5 &1 &2 & 3 &4 \\ 4& 5 &1 &2 &3 \\ 3& 4 & 5 & 1 &2 \\ 2&3 & 4 & 5 & 1 \end{bmatrix}$ It is given $A$ has only one real eigen value. Then the real eigen value of $A$ is ________

asked Jun 2 in Linear Algebra by srestha Veteran (112k points) | 83 views

0 votes

1 answer

2

Self-Doubt: Diagonalizable Matrix
$1)$ How to find a matrix is diagonalizable or not? Suppose a matrix is $A=\begin{bmatrix} \cos \Theta &\sin \Theta \\ \sin\Theta & -\cos\Theta \end{bmatrix}$ Is it diagonalizable? $2)$ What is it’s eigen spaces?

asked May 27 in Linear Algebra by srestha Veteran (112k points) | 115 views

+1 vote

1 answer

3

ISI2018-PCB-A1
Consider a $n \times n$ matrix $A=I_n-\alpha\alpha^T$, where $I_n$ is the $n\times n$ identity matrix and $\alpha$ is an $n\times 1$ column vector such that $\alpha^T\alpha=1$.Show that $A^2=A$.

asked May 12 in Linear Algebra by akash.dinkar12 Boss (40.9k points) | 55 views

+1 vote

0 answers

4

CSIR UGC NET

asked Apr 28 in Linear Algebra by Hirak Active (3.3k points) | 39 views

+1 vote

1 answer

5

Nullity of matrix
Nullity of a matrix = Total number columns – Rank of that matrix By how to calculate value of x when nullity is already given(1 in this case)

asked Jan 24 in Linear Algebra by Nandkishor3939 Active (1.1k points) | 133 views

0 votes

1 answer

6

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

asked Jan 19 in Linear Algebra by BHASHKAR (25 points) | 57 views

+1 vote

0 answers

7

#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 (2.7k points) | 66 views

0 votes

0 answers

8

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 (9.5k points) | 47 views

+2 votes

1 answer

9

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 (11.4k points) | 231 views

+2 votes

1 answer

10

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 (24.8k points) | 225 views

+1 vote

0 answers

11

Zeal Test Series 2019: Linear Algebra - Matrices

asked Nov 17, 2018 in Linear Algebra by Prince Sindhiya Loyal (5.4k points) | 66 views

0 votes

0 answers

12

Virtual Gate Test Series: Linear Algebra - Eigen Value

asked Oct 16, 2018 in Linear Algebra by Prince Sindhiya Loyal (5.4k points) | 48 views

0 votes

0 answers

13

Virtual Gate Test Series: Linear Algebra - Eigen Values of a Unity Matrix

asked Oct 15, 2018 in Linear Algebra by Prince Sindhiya Loyal (5.4k points) | 68 views

+4 votes

4 answers

14

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 (3.7k points) | 247 views

0 votes

0 answers

15

ISI2017-MMA-5
If $A$ is a $2 \times 2$ matrix such that $trace \: A = det \: A =3$, then what is the trace of $A^{-1}$? $1$ $1/3$ $1/6$ $1/2$

asked Sep 15, 2018 in Linear Algebra by jothee Veteran (97.1k points) | 35 views

0 votes

0 answers

16

ISI2017-MMA-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 Sep 15, 2018 in Linear Algebra by jothee Veteran (97.1k points) | 10 views

0 votes

0 answers

17

ISI2017-MMA-20
The number of ordered pairs $(X, Y)$, where $X$ and $Y$ are $n \times n$ real, matrices such that $XY-YX=I$ is $0$ $1$ $n$ infinite

asked Sep 15, 2018 in Linear Algebra by jothee Veteran (97.1k points) | 13 views

0 votes

0 answers

18

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 (10.3k points) | 88 views

0 votes

2 answers

19

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 (10.3k points) | 150 views

0 votes

1 answer

20

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 (13 points) | 182 views

0 votes

3 answers

21

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 Junior (913 points) | 198 views

+1 vote

1 answer

22

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 (112k points) | 154 views

+1 vote

3 answers

23

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 (112k points) | 512 views

0 votes

0 answers

24

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 (112k points) | 201 views

+2 votes

2 answers

25

ISI2017-MMA-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 Linear Algebra by jjayantamahata Active (1.3k points) | 197 views

+3 votes

1 answer

26

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 (615 points) | 288 views

+3 votes

1 answer

27

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 (615 points) | 137 views

+2 votes

2 answers

28

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 (615 points) | 162 views

+1 vote

2 answers

29

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 (615 points) | 676 views

+2 votes

2 answers

30

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 (615 points) | 2.3k views

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