19.3.17 Linear Operators

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