Quantum average

[A23]

Hi, im new to physix, I got the duty :

 

let a system be defined by the wavefunction [math]|\psi\rangle=\left(\begin{array}{c} a\\b\\c\\d\end{array}\right)[/math] and an operator

[math]A=\left(\begin{array}{cc} e&f\\f&g\end{array}\right)[/math]

 

How can [math]\langle\psi|A|\psi\rangle[/math] be computed ?