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This paper grew out of the following question: If X is a compact subset of $ {C^n}$ $ C(X) \otimes {{\mathbf{M}}_n}$-algebra of $ n \times n$) singly generated? It is shown that the answer is affirmative; in fact, $ A \otimes {{\mathbf{M}}_n}$A is a $ {C^\ast}$ $ n(n + 1)/2$ $ n(n - 1)/2$A is a separable $ {C^\ast}$ $ A \otimes K$ $ A \otimes U$K is the algebra of compact operators in a separable, infinite-dimensional Hilbert space, and U is any UHF algebra. In all these cases, the generator is explicitly constructed.