P = [{√3/2 , 1/2} {-1/2 , √3/2}], Q = PAP^T

Question

P = \(\begin{bmatrix} \frac{\sqrt{3}}{2} & \frac{1}{2} \\ \frac{-1}{2} & \frac{\sqrt{3}}{2} \\ \end{bmatrix}\), Q = PAP^T 

A = \(\begin{bmatrix} 1 & 1 \\ 0 & 1 \\ \end{bmatrix}\)^, then P^TQ²⁰⁰⁷P = \(\begin{bmatrix} a & b \\ c & d \\ \end{bmatrix}\).

Find 2a + b + 3c - 4d.

(1) 2005 

(2) 2007 

(3) 2006 

(4) 2008

Answer 1

Correct option is (1) 2005