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