If k is one of the roots of the equation x^2-25 x+24=0 such that A= [ array lll 1 & 2 & 1 3 & 2 & 3 1 & 1 & k array ] is a non-singular matrix, then A⁻¹=

Step-by-step solution

aligned x^2-25 x+24 & =0 x^2-x-24 x+24 & =0 x(x-1)-24(x-1) & =0 (x-1)(x-24) & =0 x=1,24 aligned k is one of the root of the Eq. (i), array rlrl & k & =1,24 & & k & =1, & A & = [ array lll 1 & 2 & 1 3 & 2 & 3 1 & 1 & 1 array ] |A| & =1(2-3)-2(3-3)+1(3-2) & =-1-0+1=0 |A| & =0 array k=1 , not possible, because given matrix A is singular. Now, aligned & k=24 , & A= [ array ccc 1 & 2 & 1 3 & 2 & 3 1 & 1 & 24 array ] & |A|=1(48-3)-2(72-3)+1(3-2) & =45-138+1=-92 0 & adj A= [ array ccc 45 & -69 & 1 -47 & 23 & 1 4 & 0 & -4