C11=(−1)1+1(3×2−1×1)=5 C12=(−1)1+2(2×2−3×1)=−1 C13=(−1)1+3(2×1−3×3)=−7 C21=(−1)2+1(4−3)=−1 C22=(−1)2+2(2−9)=−7 C23=(−1)2+3(1−6)=5 C31=(−1)3+1(2−9)=−7 C32=(−1)3+2(1−6)=5 C33=(−1)3+3(3−4)=−1 Co-factor of given matrix is given by- [
5,−1,−7
−1,−7,5
−7,5,−1
]=B(say) Adjoin of given matrix- ⇒BT=[
5−1−7
−1(−7)5
(−7)5−1
]=[
5,a,−7
b,−7,c
−7,d,−1
] After comparing we get, a=b=−1 and c=d=5 Thus, a+b+c+d=−1−1+5+5=8