(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Show that if [tex]{ v_1, ... , v_k} [/tex] spans [tex] V [/tex] then [tex] {T(v_1), ... , T(v_k)}[/tex] spans [tex] T(v) [/tex]

2. Relevant equations

3. The attempt at a solution

So we know that every vector in V can be written as a linear combination of [tex] v_1,...v_k [/tex] thus we only need to show that [tex] {T(v_1), ... , T(v_k)}[/tex] spans [tex] T(c_1v_1 + ... + c_kv_k) [/tex]

However, I'm not sure how to do that.

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# Homework Help: Linear Transformations and Basis

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