Minor, Cofactor, Too Adjoin Matrix

If Influenza A virus subtype H5N1 is a rectangular matrix, the youngster entries or elements aij are expressed past times M_ij in addition to are defined equally the determinant of the submatrix that resides afterwards the ith row in addition to the jth column are crossed from A. The numbers (-1)^{i + j} Mij are expressed past times C_ij called aij cofactor entries.

If Influenza A virus subtype H5N1 is whatever rectangular matrix (n 10 n) in addition to C_ij is a cofactor a_ij, in addition to then the matrix:

is called the cofactor matrix of A. Transpose This matrix is called the adjoint of A in addition to is denoted past times Adj(A).

Example:
Determine the minor, cofactor, cofactor matrix, in addition to adjoin of:

Answer:
Minor from matrix A is:
M₁₁ = 4
M₁₂ = 5
M₂₁ = 1
M₂₂ = -2

The cofactor of the matrix Influenza A virus subtype H5N1 is:
C₁₁ = (-1)¹⁺¹ M₁₁ = (1)4 = 4
C₁₂ = (-1)¹⁺² M₁₂ = (-1)5 = -5
C₂₁ = (-1)²⁺¹ M₂₁ = (-1)(1) = -1
C₂₂ = (-1)²⁺² M₂₂ = (1)(-2) = -2

The cofactor matrix is:

The adjoin of the cofactor matrix is the transpose of the cofactor matrix, therefore that:

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