Adjoint matrix
Definition: Transpose of a cofactor matrix is called Adjoint of matrix.
Adjoint is defined only for square matrices.
It involves two operations, which can be done in either order. We can take transpose of the given matrix and then replace the individual elements by their corresponding cofactors or the other way.
Transpose of a matrix:
Matrix obtained on interchanging the elements of rows and columns is called transpose of a matrix.
Transpose of is Cofactor:
The value of the determinant obtained by eliminating the row and column in which the element is present is called cofactor of the element. The cofactor is preceded with + or – sign depending upon the position of the element.
Adjoint of a 3 X 3 Matrix
Cofactor of 1 is obtained as follows:Step 1: Identify the position of the element. [(Row, column) = (i, j)]
Step 2: remove the row and column in which 1 is present.
Step 3: Write all the other elements in the determinant form
Step 4: Evaluate the determinant append with
For finding the Adjoint of 2 X 2 matrix, though we adopt the same technique, yet there is simple way to evaluate.
Adjoint of a 2 X 2 matrix:
Adjoint of a matrix is used in evaluating the multiplicative inverse of a matrix. Multiplicative inverse is defined only non-singular matrices.
