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Recent questions tagged eigen-value
1
votes
1
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61
Eigen Values of an orthogonal matrix will always be +1 and the modulus will also be always |1|?
Eigen Values of an orthogonal matrix will always be +1 and the modulus will also be always |1|? I have a doubt on this point .
Eigen Values of an orthogonal matrix will always be +1 and the modulus will also be always |1|? I have a doubt on this point .
samarpita
9.3k
views
samarpita
asked
May 9, 2022
Linear Algebra
linear-algebra
eigen-value
matrix
+
–
26
votes
1
answer
62
GATE CSE 2022 | Question: 43
Which of the following is/are the eigenvector(s) for the matrix given below? $\begin{pmatrix} - 9 & - 6 & - 2 & - 4 \\ - 8 & - 6 & - 3 & - 1 \\ 20 & 15 & 8 & 5 \\ 32 & 21 & 7 & 12 \end{pmatrix}$ ... $\begin{pmatrix} - 1 \\ 0 \\ 2 \\ 2 \end{pmatrix}$ $\begin{pmatrix} 0 \\ 1 \\ - 3 \\ 0 \end{pmatrix}$
Which of the following is/are the eigenvector(s) for the matrix given below?$$\begin{pmatrix} – 9 & – 6 & – 2 & – 4 \\ – 8 & – 6 & – 3 & – ...
Arjun
10.4k
views
Arjun
asked
Feb 15, 2022
Linear Algebra
gatecse-2022
linear-algebra
eigen-value
multiple-selects
2-marks
+
–
2
votes
1
answer
63
GATE Overflow Test Series | Mock GATE | Test 6 | Question: 35
What is the minimum value of $x^{T}Ax$ subject to $x^{T} x=1,$ if $A = \begin{bmatrix} 2022 &2021 \\ 2021 & 2022 \\ \end{bmatrix}.$ $-1$ $4043$ $1$ $-4043$
What is the minimum value of $x^{T}Ax$ subject to $x^{T} x=1,$ if $A = \begin{bmatrix}2022 &2021 \\2021 & 2022 \\\end{bmatrix}.$$-1$$4043$$1$$-4043$
Arjun
326
views
Arjun
asked
Jan 30, 2022
Linear Algebra
go2025-mockgate-6
linear-algebra
eigen-value
eigen-vector
1-mark
+
–
0
votes
1
answer
64
linear algebra - eigenvalues
What are the eigenvalues of the following matrix?
What are the eigenvalues of the following matrix?
atulcse
409
views
atulcse
asked
Jan 13, 2022
Linear Algebra
linear-algebra
eigen-value
matrix
engineering-mathematics
+
–
0
votes
0
answers
65
made easy test series - linear algebra
If 2 and -4 are the eigenvalues of a non-singular matrix A and |A| = -8, then the eigenvalues of adj(A) are x and -y. What is the value of x+y?
If 2 and -4 are the eigenvalues of a non-singular matrix A and |A| = -8, then the eigenvalues of adj(A) are x and -y. What is the value of x+y?
atulcse
418
views
atulcse
asked
Jan 13, 2022
Linear Algebra
linear-algebra
engineering-mathematics
made-easy-test-series
eigen-value
+
–
3
votes
1
answer
66
#self doubt
How to solve this question?
How to solve this question?
samarpita
601
views
samarpita
asked
Dec 28, 2021
Linear Algebra
linear-algebra
eigen-value
+
–
1
votes
1
answer
67
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.
if eigen values of matrix A = a,b,cif eigen values of matrix B = x,y,zthen is it holds every time that eigen value of A+B = a+x, b+y, c+z ?please give some reference to y...
jaswanth431
281
views
jaswanth431
asked
Dec 12, 2021
Linear Algebra
engineering-mathematics
eigen-value
linear-algebra
matrix
+
–
2
votes
1
answer
68
Linear Algebra Eigenvalues
If the eigenvalues of a 3x3 matrix A are 1,2 and 3 then inverse of A is?
If the eigenvalues of a 3x3 matrix A are 1,2 and 3 then inverse of A is?
theakatsuki4
4.7k
views
theakatsuki4
asked
Sep 16, 2021
Linear Algebra
linear-algebra
engineering-mathematics
eigen-value
matrix
+
–
18
votes
5
answers
69
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}$$The largest eigenvalue of the above matrix is __...
Arjun
15.6k
views
Arjun
asked
Feb 18, 2021
Linear Algebra
gatecse-2021-set1
linear-algebra
matrix
eigen-value
numerical-answers
2-marks
+
–
5
votes
1
answer
70
GATE Overflow Test Series | Mock GATE | Test 5 | Question: 24
Let $P$ be a matrix of order $3 \times 3$ whose elements are real numbers. If $P^2 = 0$, then the eigenvalues of $P$ are ________ $0,0,0$ $0,0,1$ $0,1,1$ $1,1,1$
Let $P$ be a matrix of order $3 \times 3$ whose elements are real numbers. If $P^2 = 0$, then the eigenvalues of $P$ are ________$0,0,0$$0,0,1$$0,1,1$$1,1,1$
gatecse
515
views
gatecse
asked
Feb 8, 2021
Linear Algebra
go2025-mockgate-5
linear-algebra
matrix
eigen-value
1-mark
+
–
2
votes
1
answer
71
GATE Overflow Test Series | Linear Algebra | Test 1 | Question: 21
The value of $'x'$ for which all the eigen values of the matrix given below $\begin{bmatrix} 2 & 3+i & 6\\ x & 3 & 2\\ 1 & 4 & 3\\ \end{bmatrix}$ are real is ________ $(i = \sqrt{-1})$ $3 + i$ $1 - 3i$ $3 - i$ $1 + 3i$
The value of $'x'$ for which all the eigen values of the matrix given below $\begin{bmatrix}2 & 3+i & 6\\x & 3 & 2\\1 & 4 & 3\\\end{bmatrix}$ are real is ________ $(i = \...
gatecse
370
views
gatecse
asked
Oct 30, 2020
Linear Algebra
go2025-linear-algebra-1
eigen-value
+
–
2
votes
1
answer
72
GATE Overflow Test Series | Linear Algebra | Test 1 | Question: 22
The eigen values of $A = \begin{bmatrix} 3 & 3 & 3 & 3 & 3\\ 3 & 3 & 3 & 3 & 3\\ 3 & 3 & 3 & 3 & 3\\ 3 & 3 & 3 & 3 & 3\\ 3 & 3 & 3 & 3 & 3 \end{bmatrix}$ are _______ $0,0,0,15,0$ $0,0,0,1,14$ $1,2,3,4,5$ $3,3,3,3,3$
The eigen values of $A = \begin{bmatrix}3 & 3 & 3 & 3 & 3\\3 & 3 & 3 & 3 & 3\\3 & 3 & 3 & 3 & 3\\3 & 3 & 3 & 3 & 3\\3 & 3 & 3 & 3 & 3\end{bmatrix}$ are _______$0,0,0,15,0...
gatecse
269
views
gatecse
asked
Oct 30, 2020
Linear Algebra
go2025-linear-algebra-1
eigen-value
+
–
2
votes
1
answer
73
GATE Overflow Test Series | Linear Algebra | Test 1 | Question: 23
If the eigen value of a $2 \times 2$ matrix $A$ are $-3$ and $-4,$ the sum of the eigen value of the matrices $(A + 2I)^{-1}$ and $(A + 8I)^{2}=$ ______
If the eigen value of a $2 \times 2$ matrix $A$ are $-3$ and $-4,$ the sum of the eigen value of the matrices $(A + 2I)^{-1}$ and $(A + 8I)^{2}=$ ______
gatecse
249
views
gatecse
asked
Oct 30, 2020
Linear Algebra
go2025-linear-algebra-1
numerical-answers
eigen-value
+
–
1
votes
1
answer
74
GATE Overflow Test Series | Linear Algebra | Test 1 | Question: 24
Let $A$ be a real $2 \times 2$ matrix. If $7+5i$ is an eigenvalue of $A$, $\text{det(A)} = \alpha,$ and $\text{trace(A)} = \beta,$ then the value of $2\alpha + 3\beta$ is _______
Let $A$ be a real $2 \times 2$ matrix. If $7+5i$ is an eigenvalue of $A$, $\text{det(A)} = \alpha,$ and $\text{trace(A)} = \beta,$ then the value of $2\alpha + 3\beta$ is...
gatecse
184
views
gatecse
asked
Oct 30, 2020
Linear Algebra
go2025-linear-algebra-1
numerical-answers
eigen-value
+
–
1
votes
3
answers
75
NIELIT 2016 MAR Scientist C - Section B: 8
The eigenvalues of the matrix $\begin{bmatrix}1 & 2\\ 4 & 3 \end{bmatrix}$ are $\text{5 and -5}$ $\text{5 and -1}$ $\text{1 and -5}$ $\text{2 and 3}$
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}$$\text{2 and 3}$
admin
661
views
admin
asked
Apr 2, 2020
Linear Algebra
nielit2016mar-scientistc
engineering-mathematics
linear-algebra
eigen-value
+
–
3
votes
3
answers
76
NIELIT 2016 DEC Scientist B (IT) - Section B: 26
Two eigenvalues of a $3\times3$ real matrix $P$ are $(2+ \sqrt-1)$ and $3$. The determinant of $P$ is ________. $0$ $1$ $15$ $-1$
Two eigenvalues of a $3\times3$ real matrix $P$ are $(2+ \sqrt-1)$ and $3$. The determinant of $P$ is ________.$0$$1$$15$$-1$
admin
981
views
admin
asked
Mar 31, 2020
Linear Algebra
nielit2016dec-scientistb-it
engineering-mathematics
linear-algebra
determinant
eigen-value
+
–
2
votes
1
answer
77
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
Let $M$ be a real $n\times n$ matrix such that for$ every$ non-zero vector $x\in \mathbb{R}^{n},$ we have $x^{T}M x 0.$ ThenSuch an $M$ cannot existSuch $Ms$ exist and th...
admin
1.4k
views
admin
asked
Feb 10, 2020
Linear Algebra
tifr2020
engineering-mathematics
linear-algebra
rank-of-matrix
eigen-value
+
–
7
votes
3
answers
78
ISI2015-MMA-39
The eigenvalues of the matrix $X = \begin{pmatrix} 2 & 1 & 1 \\ 1 & 2 & 1 \\ 1 & 1 & 2 \end{pmatrix}$ are $1,1,4$ $1,4,4$ $0,1,4$ $0,4,4$
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$$0,4,4$
Arjun
1.1k
views
Arjun
asked
Sep 23, 2019
Linear Algebra
isi2015-mma
linear-algebra
matrix
eigen-value
+
–
2
votes
2
answers
79
ISI2015-MMA-42
Let $\lambda_1, \lambda_2, \lambda_3$ denote the eigenvalues of the matrix $A \begin{pmatrix} 1 & 0 & 0 \\ 0 & \cos t & \sin t \\ 0 & - \sin t & \cos t \end{pmatrix}.$ If $\lambda_1+\lambda_2+\lambda_3 = \sqrt{2}+1$ ... $\{ - \frac{\pi}{4}, \frac{\pi}{4} \}$ $\{ - \frac{\pi}{3}, \frac{\pi}{3} \}$
Let $\lambda_1, \lambda_2, \lambda_3$ denote the eigenvalues of the matrix$$A \begin{pmatrix} 1 & 0 & 0 \\ 0 & \cos t & \sin t \\ 0 & – \sin t & \cos t \end{pmatrix}.$$...
Arjun
769
views
Arjun
asked
Sep 23, 2019
Linear Algebra
isi2015-mma
linear-algebra
matrix
eigen-value
+
–
2
votes
1
answer
80
ISI2015-MMA-62
If the matrix $A = \begin{bmatrix} a & 1 \\ 2 & 3 \end{bmatrix}$ has $1$ as an eigenvalue, then $\textit{trace}(A)$ is $4$ $5$ $6$ $7$
If the matrix $A = \begin{bmatrix} a & 1 \\ 2 & 3 \end{bmatrix}$ has $1$ as an eigenvalue, then $\textit{trace}(A)$ is$4$$5$$6$$7$
Arjun
870
views
Arjun
asked
Sep 23, 2019
Linear Algebra
isi2015-mma
linear-algebra
matrix
eigen-value
+
–
0
votes
0
answers
81
GATE MOCK 2018
An orthogonal matrix A has eigen values 1, 2 and 4, then trace of the matrix $A^T$ is ___________
An orthogonal matrix A has eigen values 1, 2 and 4, then trace of the matrix $A^T$ is ___________
Hirak
504
views
Hirak
asked
May 28, 2019
Linear Algebra
eigen-value
linear-algebra
+
–
0
votes
1
answer
82
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 $-4$ $-2$ $2$ $4$
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$$4$
akash.dinkar12
1.7k
views
akash.dinkar12
asked
May 11, 2019
Linear Algebra
isi2018-mma
engineering-mathematics
linear-algebra
eigen-value
determinant
+
–
0
votes
0
answers
83
CSIR UGC NET
Let $A$ be a $3 \times 3$ real matrix. Suppose 1 and -1 are two of the three Eigen values of $A$ and 18 is one of the Eigen values of $A^2+3 A$. Then Both $A$ and $A^2+3 A$ are invertible $A^2+3 A$ is invertible but $A$ is not invertible $A$ is invertible but $A^2+3 A$ is not invertible Both $\mathrm{A}$ and $A^2+3 A$ are not invertible.
Let $A$ be a $3 \times 3$ real matrix. Suppose 1 and -1 are two of the three Eigen values of $A$ and 18 is one of the Eigen values of $A^2+3 A$. ThenBoth $A$ and $A^2+3 A...
Hirak
568
views
Hirak
asked
Apr 28, 2019
Linear Algebra
linear-algebra
eigen-value
matrix
+
–
4
votes
1
answer
84
Vani Institute Question Bank Pg-231 chapter 6
The Eigen values of $A=\begin{bmatrix} a& 1& 0\\1 &a &1 \\0 &1 &a \end{bmatrix}$ are______ $a,a,a$ $0,a,2a$ $-a,2a,2a$ $a,a+\sqrt{2},a-\sqrt{2}$
The Eigen values of $A=\begin{bmatrix} a& 1& 0\\1 &a &1 \\0 &1 &a \end{bmatrix}$ are______$a,a,a$$0,a,2a$$-a,2a,2a$$a,a+\sqrt{2},a-\sqrt{2}$
Hirak
1.3k
views
Hirak
asked
Apr 25, 2019
Linear Algebra
engineering-mathematics
linear-algebra
eigen-value
+
–
26
votes
4
answers
85
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 _______
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 ...
Arjun
19.6k
views
Arjun
asked
Feb 7, 2019
Linear Algebra
gatecse-2019
numerical-answers
engineering-mathematics
linear-algebra
eigen-value
2-marks
+
–
0
votes
0
answers
86
Previous gate
Hemanth_13
354
views
Hemanth_13
asked
Jan 31, 2019
Linear Algebra
eigen-value
+
–
0
votes
2
answers
87
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.
Let A be a 3*3 matrix whose characteristics roots are 3,2,-1. If $B=A^2-A$ then |B|=?a)24b)-2c)12d)-12Please explain in detail.
Reshu $ingh
3.2k
views
Reshu $ingh
asked
Jan 19, 2019
Linear Algebra
linear-algebra
matrix
eigen-value
+
–
0
votes
0
answers
88
UPPCL AE 2018:58
Let $\text{A}$ be a $2 \times 2$ matrix with integer entries. Which of the following could be its eigenvalue? $\sqrt[3]{2}$ $\pi$ $\frac{1}{\sqrt{2}}$ $\sqrt{2}$
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
261
views
admin
asked
Jan 5, 2019
Linear Algebra
uppcl2018
linear-algebra
eigen-value
+
–
1
votes
0
answers
89
Eigen Values Doubt
Let there is a 2*2 Matrix and their eigen values are A and B. The eigen values of $(A+7I)^{-1}$ ?
Let there is a 2*2 Matrix and their eigen values are A and B. The eigen values of $(A+7I)^{-1}$ ?
Shamim Ahmed
519
views
Shamim Ahmed
asked
Jan 4, 2019
Linear Algebra
eigen-value
engineering-mathematics
linear-algebra
+
–
1
votes
0
answers
90
Zeal Test Series 2019: Linear Algebra - Eigen Value
Prince Sindhiya
701
views
Prince Sindhiya
asked
Dec 21, 2018
Linear Algebra
zeal
engineering-mathematics
linear-algebra
eigen-value
zeal2019
+
–
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