If [ array ccc 5 & a & -7 b & -7 & c -7 & d & -1 array ] is the adjoint of the matrix [ array lll 1 & 2 & 3 2 & 3 & 1 3 & 1 & 2 array ] , then a+b+c+d=

Step-by-step solution

aligned & 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 aligned Cofactor of given matrix is given by, [ array ccc 5 & -1 & -7 -1 & -7 & 5 -7 & 5 & -1 array ]=B( say ) Adjoint of given matrix =B^T= [ array ccc 5 & -1 & -7 -1 & -7 & 5 -7 & 5 & -1 array ]= [ array ccc 5 & a & -7 b & -7 & c -7 & d & -1 array ] After comparing, we get a=b=-1 and c=d=5 Thus, a+b+c+