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If T: V → W is a linear map and V₁, V2, ..., Vn are vectors of V so that TV₁, TV2,..., Tvn spans W, then V₁, V2,..., Vn spans V.

If T: V → W is a linear map and V₁, V2, ..., Vn are vectors of V so that TV₁, TV2,..., Tvn spans W, then V₁, V2,..., Vn spans V.

Advanced Engineering Mathematics
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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Answer TRUE or FALSE. Along with your answer, provide a

proof if true and a speci c counterexample if false.

If T : V → W is a linear map and v₁, V2, ...,Vn are vectors of V so that Tv₁, Tv2, ..., Tvn spans W, then v₁, V2, ...,Vn spans V. If T : V → W is a linear map and V₁, V2, so that V₁, V2, ...,Vn spans V, then Tv₁, Tv2, ..., Tvn spans W. Vn are vectors of V 9
Transcribed Image Text:If T : V → W is a linear map and v₁, V2, ...,Vn are vectors of V so that Tv₁, Tv2, ..., Tvn spans W, then v₁, V2, ...,Vn spans V. If T : V → W is a linear map and V₁, V2, so that V₁, V2, ...,Vn spans V, then Tv₁, Tv2, ..., Tvn spans W. Vn are vectors of V 9
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