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Recent questions tagged eigen-value

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61

Self doubt: what are eigen values of resultant matrix when add two matrices?
if eigen values of matrix A = a,b,c if eigen values of matrix B = x,y,z then is it holds every time that eigen value of A+B = a+x, b+y, c+z ? please give some reference to you answer, thankyou.

jaswanth431 asked in Linear Algebra Dec 12, 2021

250 views

2 votes

1 answer

62

Linear Algebra Eigenvalues
If the eigenvalues of a 3x3 matrix A are 1,2 and 3 then inverse of A is?

theakatsuki4 asked in Linear Algebra Sep 16, 2021

by theakatsuki4

4.7k views

16 votes

4 answers

63

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 __________.

Arjun asked in Linear Algebra Feb 18, 2021

by Arjun

15.3k views

1 vote

2 answers

64

NIELIT 2016 MAR Scientist C - Section B: 8
The eigenvalues of the matrix $\begin{bmatrix}1 & 2\\ 4 & 3 \end{bmatrix}$ are $\text{5 and -5}$ $\text{5 and -1}$ $\text{1 and -5}$ $\text{2 and 3}$

admin asked in Linear Algebra Apr 2, 2020

by admin

623 views

3 votes

3 answers

65

NIELIT 2016 DEC Scientist B (IT) - Section B: 26
Two eigenvalues of a $3\times3$ real matrix $P$ are $(2+ \sqrt-1)$ and $3$. The determinant of $P$ is ________. $0$ $1$ $15$ $-1$

admin asked in Linear Algebra Mar 31, 2020

by admin

939 views

2 votes

1 answer

66

TIFR CSE 2020 | Part A | Question: 2
Let $M$ be a real $n\times n$ matrix such that for$ every$ non-zero vector $x\in \mathbb{R}^{n},$ we have $x^{T}M x> 0.$ Then Such an $M$ cannot exist Such $Ms$ exist and their rank is always $n$ Such $Ms$ exist, but their eigenvalues are always real No eigenvalue of any such $M$ can be real None of the above

admin asked in Linear Algebra Feb 10, 2020

by admin

1.4k views

7 votes

3 answers

67

ISI2015-MMA-39
The eigenvalues of the matrix $X = \begin{pmatrix} 2 & 1 & 1 \\ 1 & 2 & 1 \\ 1 & 1 & 2 \end{pmatrix}$ are $1,1,4$ $1,4,4$ $0,1,4$ $0,4,4$

Arjun asked in Linear Algebra Sep 23, 2019

by Arjun

1.1k views

2 votes

2 answers

68

ISI2015-MMA-42
Let $\lambda_1, \lambda_2, \lambda_3$ denote the eigenvalues of the matrix $A \begin{pmatrix} 1 & 0 & 0 \\ 0 & \cos t & \sin t \\ 0 & - \sin t & \cos t \end{pmatrix}.$ If $\lambda_1+\lambda_2+\lambda_3 = \sqrt{2}+1$ ... $\{ - \frac{\pi}{4}, \frac{\pi}{4} \}$ $\{ - \frac{\pi}{3}, \frac{\pi}{3} \}$

Arjun asked in Linear Algebra Sep 23, 2019

by Arjun

765 views

2 votes

1 answer

69

ISI2015-MMA-62
If the matrix $A = \begin{bmatrix} a & 1 \\ 2 & 3 \end{bmatrix}$ has $1$ as an eigenvalue, then $\textit{trace}(A)$ is $4$ $5$ $6$ $7$

Arjun asked in Linear Algebra Sep 23, 2019

by Arjun

848 views

0 votes

0 answers

70

GATE MOCK 2018
An orthogonal matrix A has eigen values 1, 2 and 4, then trace of the matrix $A^T$ is ___________

Hirak asked in Linear Algebra May 28, 2019

by Hirak

496 views

0 votes

1 answer

71

ISI2018-MMA-14
Let $A$ be a $3× 3$ real matrix with all diagonal entries equal to $0$. If $1 + i$ is an eigenvalue of $A$, the determinant of $A$ equals $-4$ $-2$ $2$ $4$

akash.dinkar12 asked in Linear Algebra May 11, 2019

by akash.dinkar12

1.6k views

0 votes

0 answers

72

CSIR UGC NET
Let $A$ be a $3 \times 3$ real matrix. Suppose 1 and -1 are two of the three Eigen values of $A$ and 18 is one of the Eigen values of $A^2+3 A$. Then Both $A$ and $A^2+3 A$ are invertible $A^2+3 A$ is invertible but $A$ is not invertible $A$ is invertible but $A^2+3 A$ is not invertible Both $\mathrm{A}$ and $A^2+3 A$ are not invertible.

Hirak asked in Linear Algebra Apr 28, 2019

by Hirak

560 views

4 votes

1 answer

73

Vani Institute Question Bank Pg-231 chapter 6
The Eigen values of $A=\begin{bmatrix} a& 1& 0\\1 &a &1 \\0 &1 &a \end{bmatrix}$ are______ $a,a,a$ $0,a,2a$ $-a,2a,2a$ $a,a+\sqrt{2},a-\sqrt{2}$

Hirak asked in Linear Algebra Apr 25, 2019

by Hirak

1.3k views

25 votes

4 answers

74

GATE CSE 2019 | Question: 44
Consider the following matrix: $R = \begin{bmatrix} 1 & 2 & 4 & 8 \\ 1 & 3 & 9 & 27 \\ 1 & 4 & 16 & 64 \\ 1 & 5 & 25 & 125 \end{bmatrix}$ The absolute value of the product of Eigen values of $R$ is _______

Arjun asked in Linear Algebra Feb 7, 2019

by Arjun

19.3k views

0 votes

0 answers

75

Hemanth_13 asked in Linear Algebra Jan 31, 2019

351 views

0 votes

2 answers

76

Made Easy Workbook
Let A be a 3*3 matrix whose characteristics roots are 3,2,-1. If $B=A^2-A$ then |B|=? a)24 b)-2 c)12 d)-12 Please explain in detail.

Reshu $ingh asked in Linear Algebra Jan 19, 2019

3.2k views

0 votes

0 answers

77

UPPCL AE 2018:58
Let $\text{A}$ be a $2 \times 2$ matrix with integer entries. Which of the following could be its eigenvalue? $\sqrt[3]{2}$ $\pi$ $\frac{1}{\sqrt{2}}$ $\sqrt{2}$

admin asked in Linear Algebra Jan 5, 2019

by admin

251 views

1 vote

0 answers

78

Eigen Values Doubt
Let there is a 2*2 Matrix and their eigen values are A and B. The eigen values of $(A+7I)^{-1}$ ?

Shamim Ahmed asked in Linear Algebra Jan 4, 2019

by Shamim Ahmed

516 views

1 vote

0 answers

79

Zeal Test Series 2019: Linear Algebra - Eigen Value

Prince Sindhiya asked in Linear Algebra Dec 21, 2018

by Prince Sindhiya

697 views

9 votes

2 answers

80

TIFR CSE 2019 | Part A | Question: 3
$A$ is $n \times n$ square matrix for which the entries in every row sum to $1$. Consider the following statements: The column vector $[1,1,\ldots,1]^T$ is an eigen vector of $A.$ $ \text{det}(A-I) = 0.$ $\text{det}(A) = 0.$ Which of the above statements must be ... Only $(i)$ Only $(ii)$ Only $(i)$ and $(ii)$ Only $(i)$ and $(iii)$ $(i),(ii) \text{ and }(iii)$

Arjun asked in Linear Algebra Dec 18, 2018

by Arjun

3.2k views

1 vote

1 answer

81

Doubts
Eigenvalues of an Idempotentmatrix matrix A is 0 or 1 right or wrong?

sahadeo2494 asked in Linear Algebra Dec 15, 2018

453 views

2 votes

1 answer

82

NIELIT 2018-21
The value of $p$ such that the vector $\begin{bmatrix} 1 \\ 2 \\ 3 \end{bmatrix}$ is an eigen vector of the matrix $\begin{bmatrix} 4 & 1 & 2 \\ p & 2 & 1 \\ 14 & -4 & 10 \end{bmatrix}$ is $15$ $16$ $17$ $18$

Arjun asked in Linear Algebra Dec 7, 2018

by Arjun

2.2k views

1 vote

1 answer

83

Ace Test Series: Linear Algebra - Eigen Values

Sumit Kushwah asked in Linear Algebra Dec 7, 2018

by Sumit Kushwah

766 views

2 votes

0 answers

84

MadeEasy Test Series: Linear Algebra - Eigen Value
A 3 X 3 matrix P has 3 eigen values $-1 , 0.5 , 3$ What will be eigen values of $P^{2} + 2P + I$

jatin khachane 1 asked in Linear Algebra Dec 2, 2018

by jatin khachane 1

672 views

0 votes

0 answers

85

#math combat
If $A$ is $2\times 2$ matrix ,eigen value is $1,-2$ and corresponding eigen vector $[1,2]^{T}$ and $[9,1]^{T}$.find sum of element of the matrix $A.$

amit166 asked in Linear Algebra Nov 15, 2018

393 views

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