onsider the binary variable version of the fixed effects model formulated as

Yit $=$ $0+$ $1$Xit $+$ $1$D$1$i $+$ $2$D$2$i $+$ $3$D$3$i $++$ nDni $+$ uit.

$($a$)$ Suppose that n $=3.$ Show that the binary regressors and the $$constant$$

regressor are perfectly multicollineary; that is$,$ express one of the variables

D$1$iD$2$i$,$ D$3$i$,$ and X$0,$it as a perfect linear function of the others, where X$0,$it $=1$

for all i$,$ t