Hello,
I believe that there is a typo/error in the Solution of Challenge Exercise 1.3.3.
In the final step, with the substitutions, the 1/2 factor of \beta, \alpha and \gamma should not be there.
In the desired form of the matrix there is already a factor 1/2, so 1/2 is not needed.
Thus the substitution should be simply
\phi = \beta -\alpha -\gamma, \\
\omega = \gamma -\alpha
