Let U and V be vector spaces over a field F, and assume that U is...

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Let U and V be vector spaces over a field F, and assume that U is non-trivial (i.e. has at least one non-zero vector) and finite- dimensional. Let {₁,...,} be a linearly independent set in U, and let V EV.¹ Prove that there exists a linear transformation f: U →V such that f(u) = V₁ f(uk) — Vk. V1,..., Let U and V be vector spaces over a field F, and assume that U is non-trivial (i.e. has at least one non-zero vector) and finite- dimensional. Let {₁,...,} be a linearly independent set in U, and let V EV.¹ Prove that there exists a linear transformation f: U →V such that f(u) = V₁ f(uk) — Vk. V1,...,

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ANSWER Since uu is linearly independent and U is finitedimensional we can extend uu to a basis uu vv ... View the full answer