Let g : V → V be a linear transformation and let {v_1, v_2, . . . , v_n} be a basis for V . Suppose that g(v_i) = av_i for some a ∈ F. Prove: g(v) = av for all v ∈ V .
Let g : V → V be a linear transformation and let {v_1, v_2, . . . , v_n} be a basis for V . Suppose that g(v_i) = av_i for some a ∈ F. Prove: g(v) = av for all v ∈ V .
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Let g : V → V be a linear transformation and let {v_1, v_2, . . . , v_n} be a basis for V . Suppose
that g(v_i) = av_i for some a ∈ F. Prove: g(v) = av for all v ∈ V .
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