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Recent questions tagged eigen-value
3
votes
2
answers
181
Gate_2007 ME
The number of linearly independent Eigen vectors of is a) 0 b) 1 C) 2 d) infinite
The number of linearly independent Eigen vectors of is a) 0b) 1 C) 2d) infinite
Himanshu1
10.9k
views
Himanshu1
asked
Jan 2, 2016
Linear Algebra
engineering-mathematics
linear-algebra
eigen-value
+
–
3
votes
1
answer
182
GATE_2014 ME
Consider a 3 x 3 real symmetric matrix S such that two of its eigen values are a ≠ 0 , b ≠ 0 with respective Eigen vectors [ x1 x2 x3 ] , [ y1 y2 y3 ] . If a ≠ b then x1y1 + x2y2 + x3y3 is a) a b) b c) ab d) 0
Consider a 3 x 3 real symmetric matrix S such that two of its eigen values are a ≠ 0 , b ≠ 0 with respective Eigen vectors [ x1 x2 x3 ] , [ y1 y2 y3 ] . If a &ne...
Himanshu1
2.4k
views
Himanshu1
asked
Jan 2, 2016
Linear Algebra
engineering-mathematics
linear-algebra
eigen-value
+
–
3
votes
1
answer
183
Eigen Values of special matrices
A) what are the eigen values of Orthogonal matrix ? Describe general properties. B) what are the Eigen value of skew-symmetric matrix ? Describe general properties. C) Are there any speciality in Eigen values of Symmetric, Hermitian, Skew- Hermitian, Unitary . If there , describe them also.
A) what are the eigen values of Orthogonal matrix ? Describe general properties.B) what are the Eigen value of skew-symmetric matrix ? Describe general properties.C) Are ...
Himanshu1
1.6k
views
Himanshu1
asked
Jan 1, 2016
Linear Algebra
engineering-mathematics
eigen-value
linear-algebra
+
–
4
votes
3
answers
184
different independent eigen vectors
In A = (aij)nxn where aij = 1 ∀ i,j then number of different independent Eigen Vectors of A are _________ . (a) 1 (b) n-1 (c) 2 (d) n
In A = (aij)nxn where aij = 1 ∀ i,j then number of different independent Eigen Vectors of A are _________ . (a) 1(b) n-1(c) 2(d) n
Himanshu1
1.5k
views
Himanshu1
asked
Dec 31, 2015
Linear Algebra
eigen-value
linear-algebra
engineering-mathematics
+
–
3
votes
1
answer
185
Eigen values
The possible set of eigen values of a $4*4$ skew symmetric; orthogonal real matrix is A). $\pm i$ B), $(\pm i,\pm1)$ C). $\pm1$ D). $(0,\pm i)$
The possible set of eigen values of a $4*4$ skew symmetric; orthogonal real matrix is A). $\pm i$B), $(\pm i,\pm1)$C). $\pm1$D). $(0,\pm i)$
Himanshu1
1.9k
views
Himanshu1
asked
Dec 26, 2015
Linear Algebra
eigen-value
engineering-mathematics
linear-algebra
+
–
1
votes
1
answer
186
TIFR-2015-Maths-A-3
Let $A$ be a $10 \times 10$ matrix with complex entries such that all its eigenvalues are non-negative real numbers, and at least one eigenvalue is positive. Which of the following statements is always false ? There exists a matrix $B$ such that $AB-BA = B$ There exists a ... $AB-BA = A$ There exists a matrix $B$ such that $AB+BA=A$ There exists a matrix $B$ such that $AB+BA=B$
Let $A$ be a $10 \times 10$ matrix with complex entries such that all its eigenvalues are non-negative real numbers, and at least one eigenvalue is positive. Which of the...
makhdoom ghaya
616
views
makhdoom ghaya
asked
Dec 19, 2015
Linear Algebra
tifrmaths2015
linear-algebra
matrix
eigen-value
+
–
1
votes
1
answer
187
TIFR-2014-Maths-A-9
Let $A(\theta)=\begin{pmatrix} \cos \theta& \sin \theta \\ -\sin \theta& \cos \theta \end{pmatrix}$, where $\theta \in (0, 2\pi)$. Mark the correct statement below. $A(\theta)$ has eigenvectors in $\mathbb{R}^2$ for all $θ \in (0, 2\pi)$ $A(\theta)$ does not ... $θ \in (0, 2\pi)$ $A(\theta)$ has eigenvectors in $\mathbb{R}^2$ , for exactly $2$ values of $θ \in (0, 2\pi)$
Let $A(\theta)=\begin{pmatrix}\cos \theta& \sin \theta \\-\sin \theta& \cos \theta \end{pmatrix}$, where $\theta \in (0, 2\pi)$. Mark the correct statement below.$A(\thet...
makhdoom ghaya
535
views
makhdoom ghaya
asked
Dec 17, 2015
Linear Algebra
tifrmaths2014
linear-algebra
matrix
eigen-value
+
–
4
votes
3
answers
188
eigen value
Eigenvalue of matrix $A$ , $\begin{bmatrix} 2 &7 &10 \\ 5& 2 & 25\\ 1& 6 &5 \end{bmatrix}$ is $-9.33$ other eigenvalue is 1) $18.33$ 2) $-18.33$ 3) $18.33-9.33 i$ 4) $18.33+9.33i$
Eigenvalue of matrix $A$ , $\begin{bmatrix} 2 &7 &10 \\ 5& 2 & 25\\ 1& 6 &5 \end{bmatrix}$ is $-9.33$ other eigenvalue is1) $18.3...
Pooja Palod
1.0k
views
Pooja Palod
asked
Dec 16, 2015
Linear Algebra
engineering-mathematics
eigen-value
+
–
2
votes
1
answer
189
Eigen Vector
The linear operation $L(x)$ is defined by the cross product $L(x)=b \times x$, where $b=\begin{bmatrix} 0 &1 & 0 \end{bmatrix}^T$ and $x=\begin{bmatrix} x_1 &x_2 & x_3 \end{bmatrix}^T$ are three dimensional vectors. The $3 \times 3$ matrix $M$ ... of $M$ are (A) $0,+1,-1$ (B) $1,-1,1$ (C) $i,-i,1$ (D) $i,-i,0$ how to solve this..??
The linear operation $L(x)$ is defined by the cross product $L(x)=b \times x$, where $b=\begin{bmatrix} 0 &1 & 0 \end{bmatrix}^T$ and $x=\begin{bmatrix} x_1 &x_2 & x_3 \e...
Abhishekcs10
2.5k
views
Abhishekcs10
asked
Dec 16, 2015
Linear Algebra
eigen-value
linear-algebra
+
–
4
votes
1
answer
190
TIFR-2011-Maths-A-3
Let $A$ be a $5 \times 5$ matrix with real entries, then $A$ has An eigenvalue which is purely imaginary At least one real eigenvalue At least two eigenvalues which are not real At least $2$ distinct real eigenvalues
Let $A$ be a $5 \times 5$ matrix with real entries, then $A$ hasAn eigenvalue which is purely imaginaryAt least one real eigenvalueAt least two eigenvalues which are not ...
makhdoom ghaya
1.1k
views
makhdoom ghaya
asked
Dec 9, 2015
Linear Algebra
tifrmaths2011
linear-algebra
matrix
eigen-value
+
–
3
votes
2
answers
191
1. if V1 and V2 are eigenvectors that correspond to the distinct eigenvalues then they are linearly independent.
TRUE/FALSE :1. if V1 and V2 are eigenvectors that correspond to the distinct eigenvalues then they are linearly independent.2. if V1 and V2 are linearly independent eige...
yes
6.6k
views
yes
asked
Oct 21, 2015
Linear Algebra
linear-algebra
eigen-value
+
–
5
votes
2
answers
192
TIFR2010-Maths-A-10
Let $M_{n}(R)$ be the set of n x n matrices with real entries. Which of the following statements is true? Any matrix $A \in M_{4}(R)$ has a real eigenvalue Any matrix $A \in M_{5}(R)$ has a real eigenvalue Any matrix $A \in M_{2}(R)$ has a real eigenvalue None of the above
Let $M_{n}(R)$ be the set of n x n matrices with real entries. Which of the following statements is true?Any matrix $A \in M_{4}(R)$ has a real eigenvalueAny matrix $A \i...
makhdoom ghaya
1.2k
views
makhdoom ghaya
asked
Oct 11, 2015
Linear Algebra
tifrmaths2010
eigen-value
+
–
31
votes
9
answers
193
GATE CSE 2015 Set 3 | Question: 15
In the given matrix $\begin{bmatrix} 1 & -1 & 2 \\ 0 & 1 & 0 \\ 1 & 2 & 1 \end{bmatrix}$ , one of the eigenvalues is $1.$ The eigenvectors corresponding to the eigenvalue $1$ ... $\left\{a\left(- \sqrt{2},0,1\right) \mid a \neq 0, a \in \mathbb{R}\right\}$
In the given matrix $\begin{bmatrix} 1 & -1 & 2 \\ 0 & 1 & 0 \\ 1 & 2 & 1 \end{bmatrix}$ , one of the eigenvalues is $1.$ The eigenvectors corresponding to the eigenvalue...
go_editor
17.5k
views
go_editor
asked
Feb 14, 2015
Linear Algebra
gatecse-2015-set3
linear-algebra
eigen-value
normal
+
–
27
votes
5
answers
194
GATE CSE 2015 Set 1 | Question: 36
Consider the following $2 \times 2$ matrix $A$ where two elements are unknown and are marked by $a$ and $b$. The eigenvalues of this matrix are $-1$ and $7.$ What are the values of $a$ and $b$? $\qquad A = \begin{pmatrix}1 & 4\\ b&a \end{pmatrix}$ $a = 6, b = 4$ $a = 4, b = 6$ $a = 3, b = 5$ $a = 5, b = 3 $
Consider the following $2 \times 2$ matrix $A$ where two elements are unknown and are marked by $a$ and $b$. The eigenvalues of this matrix are $-1$ and $7.$ What are the...
makhdoom ghaya
6.7k
views
makhdoom ghaya
asked
Feb 13, 2015
Linear Algebra
gatecse-2015-set1
linear-algebra
eigen-value
easy
+
–
23
votes
3
answers
195
GATE CSE 2015 Set 2 | Question: 5
The larger of the two eigenvalues of the matrix $\begin{bmatrix} 4 & 5 \\ 2 & 1 \end{bmatrix}$ is _______.
The larger of the two eigenvalues of the matrix $\begin{bmatrix} 4 & 5 \\ 2 & 1 \end{bmatrix}$ is _______.
go_editor
7.5k
views
go_editor
asked
Feb 12, 2015
Linear Algebra
gatecse-2015-set2
linear-algebra
eigen-value
easy
numerical-answers
+
–
25
votes
8
answers
196
GATE IT 2006 | Question: 26
What are the eigenvalues of the matrix $P$ given below $P= \begin{pmatrix} a &1 &0 \\ 1& a& 1\\ 0&1 &a \end{pmatrix}$ $a, a -√2, a + √2$ $a, a, a$ $0, a, 2a$ $-a, 2a, 2a$
What are the eigenvalues of the matrix $P$ given below$$P= \begin{pmatrix} a &1 &0 \\ 1& a& 1\\ 0&1 &a \end{pmatrix}$$ $a, a -√2, a + √2...
Ishrat Jahan
7.4k
views
Ishrat Jahan
asked
Oct 31, 2014
Linear Algebra
gateit-2006
linear-algebra
eigen-value
normal
+
–
61
votes
8
answers
197
GATE IT 2007 | Question: 2
Let $A$ be the matrix $\begin{bmatrix}3 &1 \\ 1&2\end{bmatrix}$. What is the maximum value of $x^TAx$ where the maximum is taken over all $x$ that are the unit eigenvectors of $A?$ $5$ $\frac{(5 + √5)}{2}$ $3$ $\frac{(5 - √5)}{2}$
Let $A$ be the matrix $\begin{bmatrix}3 &1 \\ 1&2\end{bmatrix}$. What is the maximum value of $x^TAx$ where the maximum is taken over all $x$ that are the unit eigenvect...
Ishrat Jahan
16.1k
views
Ishrat Jahan
asked
Oct 29, 2014
Linear Algebra
gateit-2007
linear-algebra
eigen-value
normal
+
–
25
votes
5
answers
198
GATE CSE 2011 | Question: 40
Consider the matrix as given below. $\begin{bmatrix} 1 & 2 & 3 \\ 0 & 4 & 7 \\ 0 & 0 & 3\end{bmatrix}$ Which one of the following options provides the CORRECT values of the eigenvalues of the matrix? $1, 4, 3$ $3, 7, 3$ $7, 3, 2$ $1, 2, 3$
Consider the matrix as given below.$$\begin{bmatrix} 1 & 2 & 3 \\ 0 & 4 & 7 \\ 0 & 0 & 3\end{bmatrix}$$Which one of the following options provides the CORRECT values of...
go_editor
5.1k
views
go_editor
asked
Sep 29, 2014
Linear Algebra
gatecse-2011
linear-algebra
eigen-value
easy
+
–
41
votes
3
answers
199
GATE CSE 2014 Set 3 | Question: 4
Which one of the following statements is TRUE about every $n \times n$ matrix with only real eigenvalues? If the trace of the matrix is positive and the determinant of the matrix is negative, at least one of its eigenvalues is ... eigenvalues are positive. If the product of the trace and determinant of the matrix is positive, all its eigenvalues are positive.
Which one of the following statements is TRUE about every $n \times n$ matrix with only real eigenvalues?If the trace of the matrix is positive and the determinant of the...
go_editor
11.1k
views
go_editor
asked
Sep 28, 2014
Linear Algebra
gatecse-2014-set3
linear-algebra
eigen-value
normal
+
–
97
votes
8
answers
200
GATE CSE 2014 Set 2 | Question: 47
The product of the non-zero eigenvalues of the matrix is ____ $\begin{pmatrix} 1 & 0 & 0 & 0 & 1 \\ 0 & 1 & 1 & 1 & 0 \\ 0 & 1 & 1 & 1 & 0 \\ 0 & 1 & 1 & 1 & 0 \\ 1 & 0 & 0 & 0 & 1 \end{pmatrix}$
The product of the non-zero eigenvalues of the matrix is ____$\begin{pmatrix} 1 & 0 & 0 & 0 & 1 \\ 0 & 1 & 1 & 1 & 0 \\ 0 & 1 & 1 & 1 & 0 \\ 0 & 1 & 1 & 1 & 0 \\ 1 & 0 & ...
go_editor
36.9k
views
go_editor
asked
Sep 28, 2014
Linear Algebra
gatecse-2014-set2
linear-algebra
eigen-value
normal
numerical-answers
+
–
60
votes
4
answers
201
GATE CSE 2014 Set 1 | Question: 5
The value of the dot product of the eigenvectors corresponding to any pair of different eigenvalues of a $4-by-4$ symmetric positive definite matrix is ___________
The value of the dot product of the eigenvectors corresponding to any pair of different eigenvalues of a $4-by-4$ symmetric positive definite matrix is ___________
go_editor
14.3k
views
go_editor
asked
Sep 26, 2014
Linear Algebra
gatecse-2014-set1
linear-algebra
eigen-value
numerical-answers
normal
+
–
21
votes
3
answers
202
GATE CSE 2005 | Question: 49
What are the eigenvalues of the following $2\times 2$ matrix? $\left( \begin{array}{cc} 2 & -1\\ -4 & 5\end{array}\right)$ $-1$ and $1$ $1$ and $6$ $2$ and $5$ $4$ and $-1$
What are the eigenvalues of the following $2\times 2$ matrix? $$\left( \begin{array}{cc} 2 & -1\\ -4 & 5\end{array}\right)$$$-1$ and $1$$1$ and $6$$2$ and $5$$4$ and $-1$...
gatecse
6.0k
views
gatecse
asked
Sep 21, 2014
Linear Algebra
gatecse-2005
linear-algebra
eigen-value
easy
+
–
22
votes
4
answers
203
GATE CSE 2010 | Question: 29
Consider the following matrix $A = \left[\begin{array}{cc}2 & 3\\x & y \end{array}\right]$ If the eigenvalues of A are $4$ and $8$, then $x = 4$, $y = 10$ $x = 5$, $y = 8$ $x = 3$, $y = 9$ $x = -4$, $y =10$
Consider the following matrix $$A = \left[\begin{array}{cc}2 & 3\\x & y \end{array}\right]$$ If the eigenvalues of A are $4$ and $8$, then$x = 4$, $y = 10$$x = 5$, $y = 8...
gatecse
8.5k
views
gatecse
asked
Sep 21, 2014
Linear Algebra
gatecse-2010
linear-algebra
eigen-value
easy
+
–
28
votes
5
answers
204
GATE CSE 2002 | Question: 5a
Obtain the eigen values of the matrix$A=\begin {bmatrix} 1 & 2 & 34 & 49 \\ 0 & 2 & 43 & 94 \\ 0 & 0 & -2 & 104 \\ 0 & 0 & 0 & -1 \end{bmatrix}$
Obtain the eigen values of the matrix$$A=\begin {bmatrix} 1 & 2 & 34 & 49 \\ 0 & 2 & 43 & 94 \\ 0 & 0 & -2 & 104 \\ 0 & 0 & 0 & -1 \end{bmatrix}$$
Kathleen
4.6k
views
Kathleen
asked
Sep 15, 2014
Linear Algebra
gatecse-2002
linear-algebra
eigen-value
normal
descriptive
+
–
49
votes
7
answers
205
GATE CSE 1993 | Question: 01.1
The eigen vector $(s)$ of the matrix $\begin{bmatrix} 0 &0 &\alpha\\ 0 &0 &0\\ 0 &0 &0 \end{bmatrix},\alpha \neq 0$ is (are) $(0,0,\alpha)$ $(\alpha,0,0)$ $(0,0,1)$ $(0,\alpha,0)$
The eigen vector $(s)$ of the matrix $$\begin{bmatrix} 0 &0 &\alpha\\ 0 &0 &0\\ 0 &0 &0 \end{bmatrix},\alpha \neq 0$$ is (are)$(0,0,\alpha)$$(\alpha,0,0)$$(0,0,1)$$(0,\al...
Kathleen
11.4k
views
Kathleen
asked
Sep 13, 2014
Linear Algebra
gate1993
eigen-value
linear-algebra
easy
multiple-selects
+
–
31
votes
3
answers
206
GATE CSE 2008 | Question: 28
How many of the following matrices have an eigenvalue 1? $\left[\begin{array}{cc}1 & 0 \\0 & 0 \end{array} \right]\left[\begin{array}{cc}0 & 1 \\0 & 0 \end{array} \right] \left[\begin{array}{cc}1 & -1 \\1 & 1 \end{array} \right]$ and $\left[\begin{array}{cc}-1 & 0 \\1 & -1 \end{array} \right]$ one two three four
How many of the following matrices have an eigenvalue 1?$\left[\begin{array}{cc}1 & 0 \\0 & 0 \end{array} \right]\left[\begin{array}{cc}0 & 1 \\0 & 0 \end{array} \right] ...
Kathleen
8.5k
views
Kathleen
asked
Sep 11, 2014
Linear Algebra
gatecse-2008
eigen-value
linear-algebra
+
–
79
votes
5
answers
207
GATE CSE 2007 | Question: 25
Let A be a $4 \times 4$ matrix with eigen values -5,-2,1,4. Which of the following is an eigen value of the matrix$\begin{bmatrix} A & I \\ I & A \end{bmatrix}$, where $I$ is the $4 \times 4$ identity matrix? $-5$ $-7$ $2$ $1$
Let A be a $4 \times 4$ matrix with eigen values -5,-2,1,4. Which of the following is an eigen value of the matrix$\begin{bmatrix} A & I \\ I & A \end{bmatrix}$, where $...
priya
16.5k
views
priya
asked
Sep 2, 2014
Linear Algebra
gatecse-2007
eigen-value
linear-algebra
difficult
+
–
32
votes
5
answers
208
GATE CSE 2012 | Question: 11
Let A be the $ 2 × 2 $ matrix with elements $a_{11} = a_{12} = a_{21} = +1 $ and $ a_{22} = −1 $ . Then the eigenvalues of the matrix $A^{19}$ are $1024$ and $−1024$ $1024\sqrt{2}$ and $−1024 \sqrt{2}$ $4 \sqrt{2}$ and $−4 \sqrt{2}$ $512 \sqrt{2}$ and $−512 \sqrt{2}$
Let A be the $ 2 × 2 $ matrix with elements $a_{11} = a_{12} = a_{21} = +1 $ and $ a_{22} = −1 $ . Then the eigenvalues of the matrix $A^{19}$ are$1024$ and $−1024$$...
gatecse
11.2k
views
gatecse
asked
Aug 5, 2014
Linear Algebra
gatecse-2012
linear-algebra
eigen-value
+
–
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