Let U , V , W be finite-dimensional vector spaces. (a)If any linear map T :U W can be presented as a composition of linear maps U V W, then what can

Let U , V , W be finite-dimensional vector spaces.(a)If any linear map T :U →W can be presented as a composition of linear maps U →V →W, then what can be the dimensions of the spaces?(b) What linear maps U → W can be presented as compositions U → V → W ?