Let = {b1,b2,b3} be a basis for a vector space V and T :
Chapter 5, Problem 4E(choose chapter or problem)
Let \(\mathcal{B}=\left\{\mathbf{b}_{1}, \mathbf{b}_{2}, \mathbf{b}_{3}\right\}\) be a basis for a vector space V and \(T: V \rightarrow \mathbb{R}^{2}\) be a linear transformation with the property that
\(T\left(x_{1} \mathbf{b}_{1}+x_{2} \mathbf{b}_{2}+x_{3} \mathbf{b}_{3}\right)=\left[\begin{array}{r}2 x_{1}-4 x_{2}+5 x_{3} \\ -x_{2}+3 x_{3}\end{array}\right]\)
Find the matrix for T relative to \(\mathcal{B}\) and the standard basis for \(\mathbb{R}^{2}\).
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