1. Suppose that a list contains the values 20 44 48 55 62 66 74 88 93 99 at index positions 0 through 9. Trace the values of the variables….

## show that in the general case, exact recovery of a linear compression scheme is impossible.

1. Given some number *k*, let *k*-Richness be the following requirement: *For any finite X and every partition C *= (*C*1*, . . .**Ck *) *of X (into nonempty subsets) there exists some dissimilarity function d over X such that F*(*X**,**d*) = *C.*

Prove that, for every number *k*, there exists a clustering function that satisfies the three properties: Scale Invariance, *k*-Richness, and Consistency.

2. In this exercise we show that in the general case, exact recovery of a linear compression scheme is impossible.

3. let *A *∈R*n**,**d *be an arbitrary compression matrix where *n *≤*d*−1. Show that there exists u*,*v ∈ R*n*, u _= v such that *A*u = *A*v.