Product of all real values of ' (b ) ' such that there is no solution to the system of equations (2 x+5 y+z=19 ), (-4 x+b y+6 z=-42,-3 y-b z=81 ) is

Step-by-step solution

For no solution of given linear Equations value of given determinant is zero by Cramier's rule, So, ( array rlrl & & D= | array ccc 2 & 5 & 1 -4 & b & 6 0 & -3 & -b array | & =0 & 2 (-b^2+18 )-5(4 b)+1(12) & =0 & & -2 b^2+36-20 b+12 & =0 & & -2 b^2-20 b+48 & =0 & & b^2+20 b-24 & =0 array ) Product of roots of above equations is, ( Product = c a = -24 1 =-24 )