How Do You Find \left\langle\psi|a_1\right\rangle in Matrix Representation?

[richyw]

Homework Statement

This is quite a long problem, and I have most of it figured out, but I am getting stuck on the very last part of the problem. My problem is I do not understand how to find $\left\langle\psi|a_1\right\rangle$ in the very last line. Is $\left\langle\psi|a_1\right\rangle=(\left\langle a_1|\psi\right\rangle)^*$

Homework Equations

In a given basis $\left\langle a^{(i)}\right|$, operators are represented by $A_{i,j}=\left\langle a^{(j)}|A|a^{(i)}\right\rangle$

The Attempt at a Solution

 

[richyw]

oh dang. this doesn't recognize braket package! just one sec

 

[richyw]

ok. so sorry for posting so much stuff. but this is the only part of the question I cannot figure out and I do not have a chance to talk to anyone before the mid term. so if someone would take the time to look at it I would be very greatful.