19.3.22 Linear operators

condition: Find the norm of the matrix operator \( A: \mathbb{R}_{2}^{3} \rightarrow \mathbb{R}_{2}^{3} \) (in the Euclidean metric): \[ A=\left(\begin{array}{ccc} 15 & 0 & 0 \\ 0 & 9 & -2 \\ 0 & -2 & 3 \end{array}\right) \]