Final answer:
The set {t(v1), t(v2), t(v3)} is assumed to be linearly dependent either because the transformation t maintains the original linear dependence of the vectors, or because the vectors exhibit a specific property such as parallelism that is preserved under the transformation.
Step-by-step explanation:
Without knowing the specifics of the function t or the vectors v1, v2, and v3, we can assume for this explanation that the set {{ t(v1), t(v2), t(v3) }} is linearly dependent due to some property of t or the vectors themselves. For example, if t is a linear transformation and the vectors v1, v2, and v3 are already linearly dependent, then their images under t will also be linearly dependent. If t is the identity transformation, or if all vectors are multiples of each other, pointing along the same line, their transformed versions will maintain that dependency.
In cases where the vectors are parallel, or if they lie on the same plane while t preserves these properties, the set will also exhibit linear dependence. The concept also applies to cases where dimensions or physical quantities are involved; if the transformation t does not change these properties, the resulting set remains linearly dependent.