The below calculation is finding the expectation value of Pauli Matrix. I understood the physics how they got the below term but, I don't get that how the final result is zero in the equation . $\displaystyle \langle S_{x}\rangle=\frac{\hbar}{50}(\begin{array}{cc} -3i & 4)\left(\begin{array}{cc} 0 & 1\\ 1 & 0 \end{array}\right)\left(\begin{array}{c} 3i\\ 4 \end{array}\right)=0\end{array} \ \ \ \ \ $
After doing matrix operation, I obtain different answer.
Multiply the matrix times the last vector: $(\begin{array}{cc} -3i & 4)\left(\begin{array}{cc} 0 & 1\\ 1 & 0 \end{array}\right)\left(\begin{array}{c} 3i\\ 4 \end{array}\right)=\end{array} (\begin{array}{cc} -3i & 4)\left(\begin{array}{c} 4\\ 3i \end{array}\right)=\end{array} 0$