# Change of Bases Problem

Algebra Level pending

Consider the matrix A: $$\mathbb{R}^{3} \rightarrow \mathbb{R}^{2}$$ Given by,

$\begin{bmatrix}1&3&5 \\ 4&1&-1 \end{bmatrix}$

Let $$e_{1} \, e_{2} \, e_{3}$$ denote the standard basis and consider a new basis $$\{v_{1} , v_{2} , v_{3} \}$$ for the domain and $$\{w_{1} , w_{2} \}$$ for the co-domain which are defined in terms of the standard basis as,

$\{ v_{1} , v_{2} , v_{3} \}= \{ e_{1}+e_{2}+e_{3},e_{2}+e_{3}, e_{3} \}$ $\{ w_{1} , w_{2} \}= \{ e_{1}-e_{2}, e_{2} \}$

What is equivalent representation of L in these new bases?

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