$($a$)$ For the following matrix given by

$14$ A$=22,$

calculate $\backslash |$ A$\backslash |1,\backslash |$ A$\backslash |2,\backslash |$ A$\backslash |\backslash$infty as well as the condition numbers for each norm by hand. Is A well or poorly conditioned?$1$

$($b$)$ How many flops $($floating point operations$)$ are needed to calculate $\backslash |$ A$\backslash |1$ and $\backslash |$ A$\backslash |\backslash$infty for A in Rn$\backslash$times n$,$ assuming that taking the absolute value and determining the maximum does not contribute to the overall computational cost? By what factor will the calculation time increase when you double the matrix size?

$($c$)$ Implement a simple code that calculates $\backslash |$ A$\backslash |1$ and $\backslash |$ A$\backslash |\backslash$infty for a matrix of any size n $>=1.$ Try to do this without using loops$2!$ Using system sizes of n$1=100,$ nk$+1=2$nk$,$ k $=1,...,7,$ determine how long your code takes$3$ to calculate $\backslash |$ A$\backslash |1$ and $\backslash |$ A$\backslash |\backslash$infty for a matrix A in Rni$\backslash$times ni with random entries and report the results. Do your results confirm your estimate from $($b$)?$