Question

Consider the basis S = {v1, v2} for R2, where v1 = (1, 1) and v2 = (1, 0), and let T:R2 → R2 be the linear operator such that

T(v1) = (1, − 5) and T(v2) = (− 10, 1)

Find a formula for T(x1, x2), and use that formula to find T(11, − 6).

Answer 1

let u = \(\left[\begin{matrix}11\\-6\end{matrix}\right]\) , so to the base v1,v2, you have
\[u=\left[\begin{matrix}11\\-6\end{matrix}\right]=-6\left[\begin{matrix}1\\1\end{matrix}\right]+17\left[\begin{matrix}1\\0\end{matrix}\right]\]
got me so far??