Use mathematical induction to prove that if L is a linear transformation from V to W, then L (α1v1 + α2v2 +· · ·+αnvn)= α1L (v1) + α2L (v2)+· · ·+αnL (vn) g

The proof is shown in the explanation below.

Step-by-step explanation:

Analysis:

The proof by induction focuses on n. In this case, let n = 1, and will be a linear operator since

The exercise will show that is a linear operator on V and that is also a linear operator on V. This, follows that:

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step-by-step explanation:

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step-by-step explanation: