19.3.17 Linear operators

Condition: Prove that the following operator is linear, bounded and find its norm: \[ A: \mathbb{R}_{2}^{3} \rightarrow \mathbb{R}_{2}^{3}, \quad A\left(x_{1}, x_{2}, x_{3}\right)=\left(x_{1}, x_{2}, 0\right) \]