Adjoint of Matrix - Tutorial

Adjoint of Matrix :

Adjoint or Adjugate Matrix of a square matrix is the transpose of the matrix formed by the cofactors of elements of determinant |A|. To calculate adjoint of matrix we have to follow the procedure a) Calculate Minor for each element of the matrix. b) Form Cofactor matrix from the minors calculated. c) Form Adjoint from cofactor matrix. For an example we will use a matrix A

Step 1:

Calculate Minor for each element. To calculate the minor for an element we have to use the elements that do not fall in the same row and column of the minor element.

Similarly M₂₂ = a11xa33 - a31xa13 M₂₃ = a11xa32 - a31xa12 M₃₁ = a12xa23 - a22xa13 M₃₂ = a11xa23 - a21xa13 M₃₃ = a11xa22 - a21xa12

Step 2:

Form a matrix with the minors calculated..

Step 3:

Finding the cofactor from Minors: Cofactor: A signed minor is called cofactor. The cofactor of the element in the i^th row, j^th column is denoted by C_ij C_ij = (-1)^i+j M_ij

Step 4:

Calculate adjoint of matrix: To calculate adjoint of matrix, just put the elements in rows to columns in the cofactor matrix. i.e convert the elements in first row to first column, second row to second column, third row to third column.