Topic Content:
- Meaning of Adjoint of a Matrix
- Steps Involved in Finding the Adjoint
- Minor of a Matrix
- Minor of a 2×2 Matrix
- Minor of a 3×3 Matrix
- Cofactor of a Matrix
- Cofactor of a 2×2 Matrix
- Cofactor of a 3×3 Matrix
- Adjoint of a Matrix
- Adjoint of a 2×2 Matrix
- Adjoint of a 3×3 Matrix
The adjoint of a matrix, referred to as an adjugate matrix , is obtained by transposing the co-factor elements of the given matrix.
The adjoint of a matrix makes it easy to calculate the inverse of a matrix.
Steps Involved in Finding the Adjoint:
The three important steps involved in finding the adjoint of a matrix are:
- Find the minor matrix M of all the elements of matrix B.
- Find the cofactor matrix C of all the minor elements of matrix M.
- Find the adj B by taking the transpose of the cofactor matrix C.
Minor of a Matrix:
Each element in the determinant is associated with a minor which is formed by omitting the row and column containing the element concerned.
Minor of a 2×2 Matrix:
Example 4.2.1:
Find the minors of the matrix below:
\(\scriptsize \begin{pmatrix} 3 & 4 \\ -2 & 5 \end{pmatrix}\)
Solution
Minor of 3 = \(\scriptsize \begin{pmatrix} * & * \\ * & 5 \end{pmatrix}\)
Minor of
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