I'm sure this is a super easy question but I'm not entirely sure what these people are talking about in this section.

Let $\displaystyle \varepsilon =\{e_1 , e_2, e_3\}$ be a standard basis for $\displaystyle \mathbb{R}{^3}$. Let $\displaystyle \beta=\{b_1 , b_2, b_3\}$ for a vector space V. And let $\displaystyle T:\mathbb{R}\rightarrow{V}$ be a linear transform with the property that $\displaystyle T(x_1, x_2, x_3)=(2x_3 -x_2)b_1 -(2x_2)b_2+(x_1+3x_3)b_3$

a. Compute $\displaystyle T(e_1), T(e_2), T(e_3)$.

b. Compute $\displaystyle [T(e_1]_\beta,[T(e_2)]_\beta$, and$\displaystyle [T(e_3)]_\beta$.

c. Find the matrix for $\displaystyle T$ relative to $\displaystyle \varepsilon$ and $\displaystyle \beta$

OK I understand all of the assumptions with the exception of $\displaystyle T(x_1, x_2, x_3)=(2x_3 -x_2)b_1 -(2x_2)b_2+(x_1+3x_3)b_3$ which I can't really make sense of at the moment.