Let P = 3 2 1 2 - 1 2 3 2 , A = 1 1 0 1 and Q = P A P T . If P T Q 2007 P = a b c d then 2 a + b - 3 c - 4 d is equal to

Step-by-step solution

Given: P = 3 2 1 2 - 1 2 3 2 ∴ P P T = 3 2 1 2 - 1 2 3 2 3 2 - 1 2 1 2 3 2 = 1 0 0 1 ⇒ P P T = I Now, P T P A P T 2007 P = P T P A P T P A P T P A P T . . . P A P T ⏟ 2007   times P ⇒ P T P A P T 2007 P = A 2007 Now, A = 1 1 0 1 A 2 = 1 2 0 1 A 3 = 1 3 0 1     ⋮       ⋮       ⋮     ⋮     ⋮       ⋮       ⋮     ⋮ A 2007 = 1 2007 0 1 So, &#8658