NTA Abhyas JEE Main2020MathematicsDeterminantsPractice
The possible values of scalar k such that the matrix A - 1 - kI is singular where A = 1 0 2 0 2 1 1 0 0 , are
Options
- A− 1 2 , 2
- B− 1 , 1 2
- C1 2 , − 1 2
- D− 1 , 1
Correct answer
B. − 1 , 1 2
Step-by-step solution
A - 1 - kI = 0 A A - 1 - kI = 0 A ≠ 0 I - kA = 0 I k - A = 0 ⇒ A - 1 k . I = 0 ⇒ A - λ I = 0, where λ = 1 k ⇒ 1 - λ 0 2 0 2 - λ 1 1 0 - λ = 0 ⇒ 1 - λ - λ 2 - λ + 2 0 - 2 - λ = 0 ⇒ - λ 3 + 3 λ 2 - 2 λ - 4 + 2 λ = 0 ⇒ λ 3 − 3 λ 2 + 4 = 0 ⇒ λ = 2, 2, − 1 ⇒ k = − 1, 1 2