Consider the randomized block design (RBD) and the model:
$Y_{ij} = \mu + \tau_i + \beta_j + \epsilon_{ij}, i=1, 2, \ldots, t; j=1, 2, \ldots, b,$
with $t \geq 2, b \geq 2, \epsilon_{ij}, i.i.d. N(0, \sigma^2), \sum_{i=1}^t \tau_i =0, \sum_{j=1}^b \beta_j =0$.
In R with contr.sum to produce the design matrix ${\mathbf X}$, columns for $\tau_t$ and $\beta_b$ are not used as these parameters are expressed in terms of the other $\tau_i$ and $\beta_j$.
Let $t=$ and $b=$. The design matrix has row dimension $0$ and column dimension $-1$.
Part a) How many 1s are there in ${\mathbf X}$?
Part b) How many $-1$s are there in ${\mathbf X}$?
Part c) How many 0s are there in ${\mathbf X}$?