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\centerline{\bf Finding Matrix Elements}
\bigskip

\begin{enumerate}

\item  Carry out the following matrix calculations.

$$
\pmatrix{0&1&0\cr}\pmatrix{a_{11} & a_{12} & a_{13} \cr a_{21} &
a_{22} & a_{23} \cr a_{31} & a_{32} &
a_{33}\cr}\pmatrix{1\cr0\cr0\cr}$$ and

$$\pmatrix{0&1&0\cr}\pmatrix{a_{11} & a_{12} & a_{13} \cr a_{21} &
a_{22} & a_{23} \cr a_{31} & a_{32} &
a_{33}\cr}\pmatrix{0\cr1\cr0\cr}\quad
$$
\bigskip

\item What matrix multiplication would you do if you wanted the
answer to be $a_{13}$?

\bigskip

\item The bra-ket representation for the calulations in question 1 are

$$\matrix{\langle2\vert A\vert 1\rangle = ? & \hbox{and} & \langle2\vert A\vert 2\rangle = ?}$$

Write question number 2 in bra-ket language.
\end{enumerate}

\vfill 
\leftline{\textit{ by Corinne Manogue \& Kerry Browne}}
\leftline{copyright 2010 Corinne A. Manogue}

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