se MATLAB to determine if there is a positive integer

at most $100$ so that for

$,$ the induced $2-$norm of

as computed by MATLAB and the square root of the maximum eigenvalue of

as computed by MATLAB are not equal.

Your code should search for such a

and displays it when a value that works is found. Otherwise, it should report that no such value exists.

$($Remark$.$ Although mathematically the induced$-2$ norm of a matrix

should equal the square root of the maximum eignevalue of

$,$ there is no guarantee that MATLAB computes the former using the latter. As different numerical algorithms for the same quantity can have differences in rounding errors, we cannot expect the two computed values to be the same without knowing the algorithm MATLAB uses to compute the norm.$)$