Let A= beginpmatrix1 2 -2 -5 endpmatrix. Let α, β ∈ R be such that α A2+β A=2 I. Then α+β is equal to -

Question

Let A= beginpmatrix1 2 -2 -5 endpmatrix. Let α, β ∈ R be such that α A2+β A=2 I. Then α+β is equal to - (A) -10 (B) -6 (C) 6 (D) 10

Tardigrade Admin · Accepted Answer

Characteristic equation of matric A | A -λ I |=0 | 1-λ 2 -2 -5-λ|=0 ⇒ λ2+4 λ=1 ⇒ A 2+4 A = I ⇒ 2 A 2+8 A =2 I ....(1) Given that α A 2+β A =2 I.....(2) Comparing equation (1) (2) we get α=2, β=8 ∴ α+β=10 Ans. (D) (10)

Q. Let $A = (1 - 2 2 - 5)$ . Let $α, β \in R$ be such that $α A^{2} + β A = 2 I$ . Then $α + β$ is equal to -

$- 10$

$- 6$

6

10

Q. Let A=(1−2​2−5​). Let α,β∈R be such that αA2+βA=2I. Then α+β is equal to -

−10

−6

6

10

Characteristic equation of matric A ∣A−λI∣=0 ∣∣​1−λ−2​2−5−λ​∣∣​=0 ⇒λ2+4λ=1 ⇒A2+4A=I ⇒2A2+8A=2I....(1) Given that αA2+βA=2I.....(2) Comparing equation (1) & (2) we get α=2,β=8 ∴α+β=10 Ans. (D) (10)

Q. Let $A = (1 - 2 2 - 5)$ . Let $α, β \in R$ be such that $α A^{2} + β A = 2 I$ . Then $α + β$ is equal to -

$- 10$

$- 6$