Consider the matrix B given by

B$=[[4,7,-1],[-6,-7,4],[6,8,-3]]$

$($a$)$ Find the column$-$sum norm and the Frobenius norm of B $($by hand$).$

$($b$)$ Using Matlab, find the eigenvalues of B$^($T$)$B$,$ and thus determine the spectral norm of B by hand. As part of your answer include a write$-$up or print$-$out of the commands used in Matlab as well as the resulting output.

$($c$)$ Using Matlab, find B$^(-1),$ as well as its spectral norm. As part of your answer include a write$-$up or print$-$out of the commands used in Matlab as well as the resulting output.

$($d$)$ Using the appropriate result from $($c$),$ find the condition number of B $($by hand$)$ based on the column$-$sum norm.

$($e$)$ Using the appropriate results from $($b$)$ and $($c$),$ find the condition number of B $($by hand$),$ based on the spectral norm. Verify this result by using the 'cond' command in Matlab. As part of your answer include a write$-$up or print$-$out of the commands used in Matlab as well as the resulting output.