The number of unknown variables in the growth path model 
It's a path model of growth over time with variance-covariance matrix.
So, there are 7*8/2= 28 known variances and covariances.
But the textbook says that are 27 unknowns (7x + 7u + 6w + 6z + the variance of A1).
I don't understand why the variance of A1 must be solved.
Any help would be really appreciated!

The variance of A1 is estimated from the data, it is not constrained in the model.  (Although be warned that some SEM programs will not treat this as a parameter to be estimated, because it is exogenous.
One way to think about it. You could add a parameter z1 to A1. A1 has no predictors, so the R^2 would be zero. z1 would be estimated, and its variance would be equal to the variance of A1. These two models would be the same.
