Question

if zero is an eigenvalue of a linear transformation T, then T is not invertible. T/F justify

Answer 1

Answer on Question #40913, Math, Linear Algebra

If zero is an eigenvalue of a linear transformation $T$, then $T$ is not invertible. T/F justify

**Solution**

If zero is an eigenvalue of a linear transformation $T$, then $T$ is not invertible. **True**.

We can use the fact that an eigenvalue is a root of the characteristic polynomial

$$\det(c \cdot I - T) = 0.$$

So $c = 0$ and $\det(T) = 0$. That's why $T$ is singular and not invertible.