List of top Functional Analysis Questions on Normed Linear Spaces and Operator Norm asked in GATE MA

Let \(X = (\mathbb{R}^3, \|\cdot\|_1)\), where \(\left\|\begin{pmatrix} x \\ y \\ z \end{pmatrix}\right\|_1 = |x| + |y| + |z|\), and let \(T: X \to X\) be the linear transformation defined by \[ T\begin{pmatrix} x \\ y \\ z \end{pmatrix} = \begin{pmatrix} 1 & 1 & 3 \\ 2 & 2 & -2 \\ 1 & 3 & -3 \end{pmatrix} \begin{pmatrix} x \\ y \\ z \end{pmatrix}. \] The operator norm of \(T\) is equal to ______. (Answer in integer)