Question

Find function L given its transformation matrix and a basis

Answer 1

A linear transformation L of R^3 is given by its matrix

\[L ^{\beta}_{\beta}=\left[\begin{matrix}1 & 0 & 5 \\ 0 & 2 & 2 \\ 1 & -2 & 0\end{matrix}\right]\]

with basis

β=(1,0,0),(1,1,0),(1,1,1)
Find the function L.