Register

GATE CSE 2015 Set 1 | Question: 36

• retagged by
6,844 views
27 votes
27 votes

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 $b$?

$\qquad A = \begin{pmatrix}1 & 4\\  b&a \end{pmatrix}$

  1. $a = 6, b = 4$
  2. $a = 4, b = 6$
  3. $a = 3, b = 5$
  4. $a = 5, b = 3 $
• retagged by
User Avatar

5 Answers

0 votes
0 votes

Sum of eigen values    =  Trace of the matrix

-1+7 = 1+a

6 = 1 + a

a= 5
------------------------------------------------------------------------
 

product of eigen values = determinent of the matrix

-1 x 7 = a-4b

-7 = a-4b

-7 = 5-4b

4b = 5+7

4b = 12

b= 3

 

hope my answer helps u a lot

User Avatar
Page:
Voting & Accepting an answer helps improve the community
Answer:
← PreviousNext →
← Previous in categoryNext in category →

Related questions

23 votes
23 votes
3 answers
5
go_editor asked Feb 12, 2015
7,605 views
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 _______.
User Avatar
32 votes
32 votes
5 answers
6
makhdoom ghaya asked Feb 13, 2015
11,821 views
GATE CSE 2015 Set 1 | Question: 1‏8
In the LU decomposition of the matrix $\begin{bmatrix}2 & 2 \\ 4 & 9\end{bmatrix}$, if the diagonal elements of $U$ are both $1$, then the lower diagonal entry $l_{22}$ of $L$ is_________________.
In the LU decomposition of the matrix $\begin{bmatrix}2 & 2 \\ 4 & 9\end{bmatrix}$, if the diagonal elements of $U$ are both $1$, then the lower diagonal entry $l_{22}$ o...
User Avatar
49 votes
49 votes
7 answers
7
Kathleen asked Sep 13, 2014
11,712 views
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...
User Avatar
65 votes
65 votes
12 answers
8
makhdoom ghaya asked Feb 13, 2015
17,387 views
GATE CSE 2015 Set 1 | Question: 52
Consider the DFAs $M$ and $N$ given above. The number of states in a minimal DFA that accept the language $L(M) \cap L(N)$ is_____________.
Consider the DFAs $M$ and $N$ given above. The number of states in a minimal DFA that accept the language $L(M) \cap L(N)$ is_____________.
User Avatar
Link Copied!