3
$\begingroup$

Suppose V is the real vector space of real-valued functions with a derivative. What is the dimension of the null space of the linear map

$$Tf = x\frac{df}{dx} - 4f\;\;?$$

The basis I found for the null space is $\{x^4\}$, which gives dimension 1, but the hint for problem was that the dimension is not 1. Why is that so?

2 Answers 2