Numerical Linear Algebra with Applications

7.7 Problems

7.1 Compute the 1-norm, the ∞-norm, and the 2-norm for the following vectors. Do the calculations with paper, pencil, and a calculator.

a. $\left[\begin{array}{c}\hfill 1\hfill \\ \hfill 5\hfill \end{array}\right]$

b. $\left[\begin{array}{c}\hfill 4\hfill \\ \hfill 1\hfill \\ \hfill 3\hfill \end{array}\right]$

c. $\left[\begin{array}{c}\hfill -1\hfill \\ \hfill -9\hfill \\ \hfill -6\hfill \end{array}\right]$

d. $\left[\begin{array}{c}\hfill 1\hfill \\ \hfill 4\hfill \\ \hfill -1\hfill \\ \hfill 2\hfill \end{array}\right]$

7.2 Compute the 1-norm, the ∞-norm, the 2-norm, and the Frobenius norm for the following vectors. Except for the 2-norm, do the calculations with paper and pencil. To compute ...