Let V = {x1, x2, . . . , xv] be the set of varieties and {B1, B2, . . ., Bb] the collection of blocks for a (v, b, r, k, λ)- design. We define the incidence matrix A for the design by

a) How many l's are there in each row and column of A?
b) Let Jm×n be the m × n matrix where every entry is 1. For Jnxn we write Jn. Prove that for the incidence matrix A, A ˆ™ Jb = r J y × b and Jv ˆ™ A = k J v × b
(c) Show that

Where Iv is the v × v (multiplicative) identity,
(d) Prove that
det(A ˆ™ An) = (r - λ)n-1[r + (v - 1)λ] = (r - λ)v-lrk.

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1, ifx,EB, A (a)xb e a 0. otherwise.