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GATE | GATE-CS-2015 (Set 1) | Question 65

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Consider the following 2 × 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? 

A = | 1   4  |
      |  b  a  |

(A)

a = 3, b = 5 
 

(B)

a = 5, b = 3
 

(C)

a = 4, b = 6
 

(D)

a = 6, b = 4 
 



Answer: (B)

Explanation:

The character equation for given matrix is
| 1-λ    4 | = 0
|  b    a-λ|
(1-λ)*(a-λ) - 4b = 0
Putting λ = -1,
=> (1 - (-1)) * (a - (-1)) - 4b = 0
=> 2a + 2 - 4b = 0
=> 2b - a = 1
Putting λ = 7,
=> (1 - 7) * (a - 7) - 4b = 0
=> -6a + 42 - 4b = 0
=> 2b + 3a = 21
Solving the above two equations, we get
a = 5, b = 3


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Last Updated : 28 Jun, 2021
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