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Let $$ A = \left( \begin{array}{ccccc} 2 & -3 & 0 & 2 & 1 \\ 2 & -1 & -1 & 0 & 3 \\ -1 & -1 & -3 & 1 & 2 \\ -1 & -1 & -1 & -1 & -2 \\ -1 & -2 & 0 & 1 & -2 \end{array} \right). $$ Compute the $\infty$-norm of $A$.
$$||A||{\infty} = max \Bigg{{} \sum{j=1}^{n} |a_{ij}| \ \Bigg{|} \ 1 \leq i \leq n \Bigg{}} \\$$
$$||A||{\infty} = \sum{j=1}^{n} |a_{1j}| = \sum_{j=1}^{n} |a_{3j}| = \boxed{8}$$
$$ ||A||{\infty} = \sum{j=1}^{n} |a_{1j}| = \sum_{j=1}^{n} |a_{3j}| = 8 $$
Comments
$$||A||{\infty} = max \Bigg{{} \sum{j=1}^{n} |a_{ij}| \ \Bigg{|} \ 1 \leq i \leq n \Bigg{}} \\$$
$$||A||{\infty} = \sum{j=1}^{n} |a_{1j}| = \sum_{j=1}^{n} |a_{3j}| = \boxed{8}$$
$$ ||A||{\infty} = \sum{j=1}^{n} |a_{1j}| = \sum_{j=1}^{n} |a_{3j}| = 8 $$