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Recent questions tagged eigen-value
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Memory Based GATE DA 2024 | Question: 6
Consider the matrix \[ \begin{bmatrix} 2 & -1 \\ 3 & 1 \end{bmatrix} \] What is the nature of the eigenvalues of the given matrix? Both eigenvalues are positive. One eigenvalue is negative. Eigenvalues are complex conjugate pairs. None of the above.
GO Classes
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Linear Algebra
Feb 5
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GO Classes
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gate2024-da-memory-based
goclasses
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4
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0
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2
GO Classes Test Series 2024 | Mock GATE | Test 11 | Question: 30
Let $A$ be a matrix defined as $A=u v^T$, where $u$ and $v$ are column vectors of dimension $3 \times 1$. The resulting matrix $A$ will be of dimension $3 \times 3$. What are the maximum number of nonzero eigenvalues possible for the matrix $A?$
GO Classes
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Linear Algebra
Jan 13
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GO Classes
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0
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3
Diagonalization of Matrix
Debargha Mitra Roy
asked
in
Linear Algebra
Jan 11
by
Debargha Mitra Roy
46
views
matrix
linear-algebra
eigen-value
0
votes
0
answers
4
Diagonalization of Matrix - Orthogonal Transformation
Consider a symmetric matrix $M=\begin{bmatrix} \frac{1}{3} & 0 & \frac{2}{3}\\ 0&1 &0 \\ \frac{2}{3}&0 & \frac{1}{3} \end{bmatrix}$. An orthogonal matrix $O$ which can diagonalize this matrix by an orthogonal transformation $O^TMO$ is given by $O = $ ______
Debargha Mitra Roy
asked
in
Linear Algebra
Jan 11
by
Debargha Mitra Roy
71
views
linear-algebra
eigen-value
matrix
0
votes
0
answers
5
Function of Matrix - Sylvester Theorem & Cayley-Hamilton Theorem
$Prove\ that,\ sin^2A+cos^2A=1,\ where \ A=\begin{bmatrix} 1&2 \\ -1&4 \end{bmatrix}.$
Debargha Mitra Roy
asked
in
Linear Algebra
Jan 10
by
Debargha Mitra Roy
49
views
eigen-value
0
votes
0
answers
6
Function of Matrix - Sylvester Theorem
$Given \ A=\begin{bmatrix} 1&20&0 \\ -1&7&1 \\ 3&0&-2 \end{bmatrix},\ find\ tan\ A\ .$
Debargha Mitra Roy
asked
in
Linear Algebra
Jan 10
by
Debargha Mitra Roy
30
views
eigen-value
0
votes
0
answers
7
Linear Algebra, Eigen Vales & Eigen Vectors
$If \ A = \begin{pmatrix} 1&1 \\ 1&0 \end{pmatrix},\ \alpha M_1+\beta M_2+\gamma M_3,\ where \ M_1 = L_{2x2},\ M_2 = \begin{pmatrix} 0&1 \\ 1&1 \end{pmatrix}\ and \ M_3 = \begin{pmatrix} 1&1 \\ 1&1 \end{pmatrix} \ then \ -$ ... $\alpha = 1,\ \beta = -1,\ \gamma = 2$ D. $\alpha = -1,\ \beta = 1,\ \gamma = 2$
Debargha Mitra Roy
asked
in
Linear Algebra
Jan 8
by
Debargha Mitra Roy
94
views
engineering-mathematics
linear-algebra
eigen-value
matrix
0
votes
0
answers
8
#linear algebra#eigen values
rank of a matrix = number of non-zero eigenvalues always?
Dknights
asked
in
Linear Algebra
Dec 4, 2023
by
Dknights
84
views
eigen-value
0
votes
3
answers
9
GATE Data Science and Artificial Intelligence 2024 | Sample Paper | Question: 17
For matrix $H=\left[\begin{array}{cc}9 & -2 \\ -2 & 6\end{array}\right]$, one of the eigenvalues is $5$. Then, the other eigenvalue is $12$ $10$ $8$ $6$
admin
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Linear Algebra
Oct 22, 2023
by
admin
1.3k
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gateda-sample-paper-2024
linear-algebra
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0
votes
1
answer
10
rbr practice questions
Is the product of eigen values of a matrix equal to its determinant true for all the matrices?
vanshikha020
asked
in
Linear Algebra
Jul 1, 2023
by
vanshikha020
441
views
matrix
eigen-value
1
vote
1
answer
11
matrix maths
1 -3 3 0 -5 6 0 -3 4 a 3*3 matrix is given if x,y, z are the eigan value then find xy+yz+ax? my approch if i do row transformation in c2->c2+c3 and then c2->4c2-c3, so my matrix become upper tringular matrix then ... -6 but using genral method via substract lemda from diagonal element and then determinant of matrix getting answer -3 which one is correct and why not other one
jugnu1337
asked
in
Linear Algebra
May 14, 2023
by
jugnu1337
355
views
linear-algebra
eigen-value
9
votes
2
answers
12
GO Classes 2024 | Weekly Quiz 7 | Linear Algebra | Question: 5
Suppose that the characteristic polynomial of $\text{A}$ is $ p(\lambda)=\lambda(\lambda-2)(\lambda-3)^2. $ Which of the following can you determine from this information? The rank of $\text{A}$. Whether $\text{A}$ is symmetric. Whether $\text{A}$ is diagonalizable. The eigenvalues of $\text{A}$.
GO Classes
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in
Linear Algebra
Apr 5, 2023
by
GO Classes
748
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goclasses2024_wq7
goclasses
linear-algebra
eigen-value
rank-of-matrix
multiple-selects
1-mark
12
votes
2
answers
13
GO Classes 2024 | Weekly Quiz 7 | Linear Algebra | Question: 8
Suppose that $A$ is a $3 \times 3$ real-symmetric matrix with eigenvalues $\lambda_1=1$, $\lambda_2=-1, \lambda_3=-2$, and corresponding eigenvectors $x_1, x_2, x_3.$ You are given that $x_1=\left(\begin{array}{l}1 \\ 0 \\ 1\end{array}\right)$ ... $x_3 =\left(\begin{array}{c} 0 \\ 0 \\ 0 \end{array}\right)$
GO Classes
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in
Linear Algebra
Apr 5, 2023
by
GO Classes
814
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goclasses2024_wq7
goclasses
linear-algebra
eigen-value
multiple-selects
1-mark
12
votes
3
answers
14
GO Classes 2024 | Weekly Quiz 7 | Linear Algebra | Question: 9
Consider two statements below - Statement $1: $ If $A$ is invertible and $\lambda$ is an eigenvalue of $A$, then $\frac{1}{\lambda}$ is an eigenvalue of $A^{-1}$. Statement $2:$ Let $A$ be a real skew- ... true but Statement $2$ is false Statement $2$ is true but Statement $1$ is false Both statements are true Both statements are false
GO Classes
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Linear Algebra
Apr 5, 2023
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GO Classes
676
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goclasses2024_wq7
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eigen-value
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8
votes
1
answer
15
GO Classes 2024 | Weekly Quiz 7 | Linear Algebra | Question: 17
You have a matrix $A$ ... $3$ eigenvalues of $A?$
GO Classes
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in
Linear Algebra
Apr 5, 2023
by
GO Classes
477
views
goclasses2024_wq7
numerical-answers
goclasses
linear-algebra
eigen-value
2-marks
0
votes
0
answers
16
GATE EE 2007
The linear operation L(x) is defined by the cross product L(x) = b x X, where b=[0 1 0] and X=[xxx]' are three dimensional vectors. The 3 x 3 matrix M of this operation satisfies: L(x)=M (x1 x2 x3)' Then the eigen values of M are: (a) 0, +1,-1 (b) 1, -1, 1 (c) i, -i, 0 (d) i, -i, 1 [EE, GATE-2007, 2 marks]
Priyanshu Karmakar
asked
in
Linear Algebra
Mar 30, 2023
by
Priyanshu Karmakar
312
views
linear-algebra
eigen-value
22
votes
2
answers
17
GO Classes Weekly Quiz 6 | Linear Algebra | Question: 14
Mark all the INCORRECT statements Let $A$ be the matrix of a rotation by angle $30$ degree. That is, for any vector $x,$ the angle between $x$ and $A x$ is always $30$ degree. Then $A$ has no real eigenvalues. Let $A$ ... eigenvalues $\lambda=1,2,3$, then $A$ is singular. If $A$ is a symmetric matrix, then all its eigenvectors are orthogonal.
GO Classes
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in
Linear Algebra
Mar 29, 2023
by
GO Classes
1.1k
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goclasses2024_wq6
goclasses
linear-algebra
eigen-value
multiple-selects
1-mark
13
votes
3
answers
18
GO Classes Weekly Quiz 6 | Linear Algebra | Question: 22
A three-by-three matrix $B$ is known to have eigenvalues $0,1$ and $2.$ This information is enough to find which one of these (give the answers where possible): The rank of $B$ The determinant of $B^T B$ The eigenvalues of $B^T B$ The eigenvalues of $\left(B^2+I\right)^{-1}$
GO Classes
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Linear Algebra
Mar 29, 2023
by
GO Classes
1.1k
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goclasses2024_wq6
goclasses
linear-algebra
eigen-value
multiple-selects
2-marks
15
votes
3
answers
19
GO Classes Weekly Quiz 6 | Linear Algebra | Question: 25
Let $u \in \mathbb{R}^n$ be such that $u^T u=1$ and set $A=u u^T$. What will be the sum of all eigenvalues of $A?$
GO Classes
asked
in
Linear Algebra
Mar 29, 2023
by
GO Classes
871
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goclasses2024_wq6
numerical-answers
goclasses
linear-algebra
eigen-value
2-marks
0
votes
1
answer
20
#Eigen Vectors
Find the eigen values and eigen vector of the following matrix????
Çșȇ ʛấẗẻ
asked
in
Mathematical Logic
Mar 21, 2023
by
Çșȇ ʛấẗẻ
1.2k
views
eigen-value
linear-algebra
engineering-mathematics
matrix
8
votes
4
answers
21
GATE CSE 2023 | Question: 20
Let $A$ be the adjacency matrix of the graph with vertices $\{1,2,3,4,5\}.$ Let $\lambda_{1}, \lambda_{2}, \lambda_{3}, \lambda_{4}$, and $\lambda_{5}$ be the five eigenvalues of $A$. Note that these eigenvalues need not be distinct. The value of $\lambda_{1}+\lambda_{2}+\lambda_{3}+\lambda_{4}+\lambda_{5}=$____________
admin
asked
in
Linear Algebra
Feb 15, 2023
by
admin
12.6k
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gatecse-2023
linear-algebra
eigen-value
numerical-answers
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