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Let A = 1 2 - 1 4 . If A - 1 = α I + β A , α , β ∈ R , I is a 2 × 2 identity matrix, then 4 α - β is equal to :

Options

  1. A5
  2. B8 3
  3. C2
  4. D4

Correct answer

D. 4

Step-by-step solution

Given, A = 1 2 - 1 4 ⇒ A = 6 So, A - 1 = adj A A = 1 6 4 - 2 1 1 = 2 3 - 1 3 1 6 1 6 Here, 2 3 - 1 3 1 6 1 6 = α 0 0 α + β 2 β - β 4 β α + β = 2 3 β = - 1 6 ⇒ α = 2 3 + 1 6 = 5 6 Hence, 4 α - β = 4 1 = 4

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