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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.
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 ...
GO Classes
235
views
GO Classes
asked
Feb 4
Linear Algebra
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goclasses
linear-algebra
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4
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1
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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 $A?$
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...
GO Classes
715
views
GO Classes
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Jan 13
Linear Algebra
goclasses2024-mockgate-11
goclasses
numerical-answers
linear-algebra
eigen-value
1-mark
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0
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0
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3
Diagonalization of Matrix
Debargha Mitra Roy
54
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Debargha Mitra Roy
asked
Jan 11
Linear Algebra
matrix
linear-algebra
eigen-value
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0
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0
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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 = $ ______
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 di...
Debargha Mitra Roy
83
views
Debargha Mitra Roy
asked
Jan 11
Linear Algebra
linear-algebra
eigen-value
matrix
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1
votes
0
answers
5
Function of Matrix - Sylvester Theorem & Cayley-Hamilton Theorem
$Prove\ that,\ sin^2A+cos^2A=1,\ where \ A=\begin{bmatrix} 1&2 \\ -1&4 \end{bmatrix}.$
$Prove\ that,\ sin^2A+cos^2A=1,\ where \ A=\begin{bmatrix} 1&2 \\ -1&4 \end{bmatrix}.$
Debargha Mitra Roy
55
views
Debargha Mitra Roy
asked
Jan 10
Linear Algebra
eigen-value
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–
0
votes
0
answers
6
Function of Matrix - Sylvester Theorem
$Given \ A=\begin{bmatrix} 1&20&0 \\ -1&7&1 \\ 3&0&-2 \end{bmatrix},\ find\ tan\ A\ .$
$Given \ A=\begin{bmatrix} 1&20&0 \\ -1&7&1 \\ 3&0&-2 \end{bmatrix},\ find\ tan\ A\ .$
Debargha Mitra Roy
37
views
Debargha Mitra Roy
asked
Jan 10
Linear Algebra
eigen-value
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–
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. $\alpha = -1,\ \beta = 1,\ \gamma = 2$
$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 =...
Debargha Mitra Roy
102
views
Debargha Mitra Roy
asked
Jan 8
Linear Algebra
engineering-mathematics
linear-algebra
eigen-value
matrix
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0
votes
0
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8
#linear algebra#eigen values
rank of a matrix = number of non-zero eigenvalues always?
rank of a matrix = number of non-zero eigenvalues always?
Dknights
90
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Dknights
asked
Dec 4, 2023
Linear Algebra
eigen-value
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–
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 $12$ $10$ $8$ $6$
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$$6$
admin
1.4k
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admin
asked
Oct 21, 2023
Linear Algebra
gateda-sample-paper-2024
linear-algebra
eigen-value
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0
votes
1
answer
10
rbr practice questions
Is the product of eigen values of a matrix equal to its determinant true for all the matrices?
Is the product of eigen values of a matrix equal to its determinant true for all the matrices?
vanshikha020
445
views
vanshikha020
asked
Jul 1, 2023
Linear Algebra
matrix
eigen-value
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–
1
votes
1
answer
11
matrix maths
1 -3 3 0 -5 6 0 -3 4 a 3*3 matrix is given if x,y, z are the eigan value then find xy+yz+ax? my approch if i do row transformation in c2->c2+c3 and then c2->4c2-c3, so my matrix become upper tringular matrix then ... -6 but using genral method via substract lemda from diagonal element and then determinant of matrix getting answer -3 which one is correct and why not other one
1 -3 30 -5 60 -3 4 a 3*3 matrix is given if x,y, z are the eigan value then find xy+yz+ax? my approch… if i do row transformation in c2->c2+c3and then c2-...
jugnu1337
362
views
jugnu1337
asked
May 14, 2023
Linear Algebra
linear-algebra
eigen-value
+
–
9
votes
2
answers
12
GO Classes 2024 | Weekly Quiz 7 | Linear Algebra | Question: 5
Suppose that the characteristic polynomial of $\text{A}$ is $ p(\lambda)=\lambda(\lambda-2)(\lambda-3)^2. $ Which of the following can you determine from this information? The rank of $\text{A}$. Whether $\text{A}$ is symmetric. Whether $\text{A}$ is diagonalizable. The eigenvalues of $\text{A}$.
Suppose that the characteristic polynomial of $\text{A}$ is$$p(\lambda)=\lambda(\lambda-2)(\lambda-3)^2.$$Which of the following can you determine from this information?T...
GO Classes
769
views
GO Classes
asked
Apr 5, 2023
Linear Algebra
goclasses2024_wq7
goclasses
linear-algebra
eigen-value
rank-of-matrix
multiple-selects
1-mark
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–
12
votes
2
answers
13
GO Classes 2024 | Weekly Quiz 7 | Linear Algebra | Question: 8
Suppose that $A$ is a $3 \times 3$ real-symmetric matrix with eigenvalues $\lambda_1=1$, $\lambda_2=-1, \lambda_3=-2$, and corresponding eigenvectors $x_1, x_2, x_3.$ You are given that $x_1=\left(\begin{array}{l}1 \\ 0 \\ 1\end{array}\right)$ ... $x_3 =\left(\begin{array}{c} 0 \\ 0 \\ 0 \end{array}\right)$
Suppose that $A$ is a $3 \times 3$ real-symmetric matrix with eigenvalues $\lambda_1=1$, $\lambda_2=-1, \lambda_3=-2$, and corresponding eigenvectors $x_1, x_2, x_3.$You ...
GO Classes
840
views
GO Classes
asked
Apr 5, 2023
Linear Algebra
goclasses2024_wq7
goclasses
linear-algebra
eigen-value
multiple-selects
1-mark
+
–
12
votes
3
answers
14
GO Classes 2024 | Weekly Quiz 7 | Linear Algebra | Question: 9
Consider two statements below - Statement $1: $ If $A$ is invertible and $\lambda$ is an eigenvalue of $A$, then $\frac{1}{\lambda}$ is an eigenvalue of $A^{-1}$. Statement $2:$ Let $A$ be a real skew- ... true but Statement $2$ is false Statement $2$ is true but Statement $1$ is false Both statements are true Both statements are false
Consider two statements below -Statement $1: $ If $A$ is invertible and $\lambda$ is an eigenvalue of $A$, then $\frac{1}{\lambda}$ is an eigenvalue of $A^{-1}$.Statement...
GO Classes
706
views
GO Classes
asked
Apr 5, 2023
Linear Algebra
goclasses2024_wq7
goclasses
linear-algebra
eigen-value
1-mark
+
–
8
votes
1
answer
15
GO Classes 2024 | Weekly Quiz 7 | Linear Algebra | Question: 17
You have a matrix $A$ ... $3$ eigenvalues of $A?$
You have a matrix $A$ with the factorization:$$A=\underbrace{\left(\begin{array}{ccc}1 & & \\3 & 2 & \\1 & -1 & 2\end{array}\right)}_B \quad \underbrace{\left(\begin{arra...
GO Classes
502
views
GO Classes
asked
Apr 5, 2023
Linear Algebra
goclasses2024_wq7
numerical-answers
goclasses
linear-algebra
eigen-value
2-marks
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0
votes
0
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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]
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 s...
Priyanshu Karmakar
317
views
Priyanshu Karmakar
asked
Mar 30, 2023
Linear Algebra
linear-algebra
eigen-value
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–
0
votes
1
answer
17
#Eigen Vectors
Find the eigen values and eigen vector of the following matrix????
Find the eigen values and eigen vector of the following matrix????
Çșȇ ʛấẗẻ
1.2k
views
Çșȇ ʛấẗẻ
asked
Mar 21, 2023
Mathematical Logic
eigen-value
linear-algebra
engineering-mathematics
matrix
+
–
9
votes
4
answers
18
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 $\lambda_{1}+\lambda_{2}+\lambda_{3}+\lambda_{4}+\lambda_{5}=$____________
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 eigenva...
admin
12.7k
views
admin
asked
Feb 15, 2023
Linear Algebra
gatecse-2023
linear-algebra
eigen-value
numerical-answers
1-mark
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