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Recent questions tagged eigen-value

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$
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0 votes
1 answer
64
linear algebra - eigenvalues
What are the eigenvalues of the following matrix?
What are the eigenvalues of the following matrix?
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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?
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3 votes
1 answer
66
#self doubt
How to solve this question?
How to solve this question?
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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?
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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 __...
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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$
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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 = \...
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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...
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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}=$ ______
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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...
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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}$
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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$$-1$
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7 votes
3 answers
78
ISI2015-MMA-39
The eigenvalues of the matrix $X = \begin{pmatrix} 2 & 1 & 1 \\ 1 & 2 & 1 \\ 1 & 1 & 2 \end{pmatrix}$ are $1,1,4$ $1,4,4$ $0,1,4$ $0,4,4$
The eigenvalues of the matrix $X = \begin{pmatrix} 2 & 1 & 1 \\ 1 & 2 & 1 \\ 1 & 1 & 2 \end{pmatrix}$ are$1,1,4$$1,4,4$$0,1,4$$0,4,4$
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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$$7$
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0 votes
0 answers
81
GATE MOCK 2018
An orthogonal matrix A has eigen values 1, 2 and 4, then trace of the matrix $A^T$ is ___________
An orthogonal matrix A has eigen values 1, 2 and 4, then trace of the matrix $A^T$ is ___________
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0 votes
1 answer
82
ISI2018-MMA-14
Let $A$ be a $3× 3$ real matrix with all diagonal entries equal to $0$. If $1 + i$ is an eigenvalue of $A$, the determinant of $A$ equals $-4$ $-2$ $2$ $4$
Let $A$ be a $3× 3$ real matrix with all diagonal entries equal to $0$. If $1 + i$ is an eigenvalue of $A$, the determinant of $A$ equals$-4$$-2$$2$$4$
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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$$a,a+\sqrt{2},a-\sqrt{2}$
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26 votes
4 answers
85
GATE CSE 2019 | Question: 44
Consider the following matrix: $R = \begin{bmatrix} 1 & 2 & 4 & 8 \\ 1 & 3 & 9 & 27 \\ 1 & 4 & 16 & 64 \\ 1 & 5 & 25 & 125 \end{bmatrix}$ The absolute value of the product of Eigen values of $R$ is _______
Consider the following matrix:$R = \begin{bmatrix} 1 & 2 & 4 & 8 \\ 1 & 3 & 9 & 27 \\ 1 & 4 & 16 & 64 \\ 1 & 5 & 25 & 125 \end{bmatrix}$The absolute value of the product ...
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0 votes
0 answers
86
Previous gate
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0 votes
2 answers
87
Made Easy Workbook
Let A be a 3*3 matrix whose characteristics roots are 3,2,-1. If $B=A^2-A$ then |B|=? a)24 b)-2 c)12 d)-12 Please explain in detail.
Let A be a 3*3 matrix whose characteristics roots are 3,2,-1. If $B=A^2-A$ then |B|=?a)24b)-2c)12d)-12Please explain in detail.
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0 votes
0 answers
88
UPPCL AE 2018:58
Let $\text{A}$ be a $2 \times 2$ matrix with integer entries. Which of the following could be its eigenvalue? $\sqrt[3]{2}$ $\pi$ $\frac{1}{\sqrt{2}}$ $\sqrt{2}$
Let $\text{A}$ be a $2 \times 2$ matrix with integer entries. Which of the following could be its eigenvalue?$\sqrt[3]{2}$$\pi$$\frac{1}{\sqrt{2}}$$\sqrt{2}$
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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 $(A+7I)^{-1}$ ?
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