Adjoint of Matrix

▶Cofactor Matrix

 ▷A_ij (= (-1)^(1+j) × det(M_ij)) 로 이루어진 Matrix

 

▶Adjoint of A ( Adj(A) )

 ▷Cofactor Matrix를 transpose 한 Matrix

 ▷A×Adj(A) = det(A)×I = Adj(A)×A

 ▷A^-1 = 1/det(A)×Adj(A)

 ▶Cramer's Rule

  ▷x_i = det(A_i) / det(A)

  ▷det(A_i) = (b_1)(A_1i) + (b_2)(A_2i) + .. +(b_n)(A_ni)

  ▷Pf) x = (A^-1)(b) = 1/det(A) × Adj(A) × b