# Find a basis for $V$ for which it is the dual basis

Let $V=(\Bbb R^3)$ and define $f_1, f_2, f_3 \in V^*$ as follows:

$$f_1(x, y, z) = x − 2y,f_2(x, y, z) = x + y + z, f_3(x, y, z) = y − 3z.$$

Prove that $\{f_1, f_2, f_3\}$ is a basis for $V^*$, and then find a basis for $V$ for which it is the dual basis.

My work for the part (a):