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Let α ,β be two non-zero real numbers and v1 , v2 be two non-zero real vectors of size 3 x 1. Suppose that v1 and v2 satisfy . Let A be the 3 x 3 matrix given by . The eigenvalues of A are
  • a)
  • b)
  • c)
    0, α + β, α - β
  • d)
    0, α, β
Correct answer is option 'D'. Can you explain this answer?
Most Upvoted Answer
Let α ,β be two non-zero real numbers and v1 , v2 be two non-zero r...
Given : α, β → Two non-zero real numbers.
v1, v2 → Two non-zero real numbers of size 3 x 1
..........(i)
Every square matrix satisfies the following equation
[A - λI ][X] = 0
Ax = λx …(ii)
By equation (i) and (ii),
⇒ A = α is Eigen value of matrix A.
By equation (i) and (ii),
Av2 = αv1v2v1T + βv2v2v2T
Av2 = 0 + βv2
Av2 = βv2
⇒ A = β is eigen value of matrix A
Only option (D) satisfies.
Hence, the correct option is (D).
Free Test
Community Answer
Let α ,β be two non-zero real numbers and v1 , v2 be two non-zero r...
Given : α, β → Two non-zero real numbers.
v1, v2 → Two non-zero real numbers of size 3 x 1
..........(i)
Every square matrix satisfies the following equation
[A - λI ][X] = 0
Ax = λx …(ii)
By equation (i) and (ii),
⇒ A = α is Eigen value of matrix A.
By equation (i) and (ii),
Av2 = αv1v2v1T + βv2v2v2T
Av2 = 0 + βv2
Av2 = βv2
⇒ A = β is eigen value of matrix A
Only option (D) satisfies.
Hence, the correct option is (D).
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Let α ,β be two non-zero real numbers and v1 , v2 be two non-zero real vectors of size 3 x 1. Suppose that v1 and v2 satisfy . Let A be the 3 x 3 matrix given by . The eigenvalues of A area)b)c)0, α + β, α - βd)0, α, βCorrect answer is option 'D'. Can you explain this answer?
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