Consider the following matrix

$=30000131313131303000131313131300300131313131300030131313131300003131313131355555155555555551555555555515555555555155555555551$

The MATLAB code to produce $$

is given by:

P$=[3*$eye$(5),5*$ones$(5)$;$13*$ones$(5),5*$ones$(5)-4*$eye$(5)]$

Calculate the dot product of row $6$ and column $2$ of $$

$.$

Let $=31$

$.$ Calculate det$()$

$.$

Calculate rank$(+4)$

$.$