Describe Minors And Cofactors.

Minor of an element is defined as the determinant obtained by deleting the row and column in which that element lies in the matrix. They are one of the most important concepts to determine the adjoint of a matrix. The minors when multiplied by (-1)^{i + j} gives the cofactors, where i is the row number and j is the column number. Let's understand in detail.

Answer: The minors and cofactors are the important concepts used to determine the adjoint and hence, the inverse of a matrix.

Let us understand in detail.

Explanation:

The minor of an element is defined as the determinant obtained by deleting the row and column in which that element lies in the matrix. 

For example in the matrix below, the minor of 2 is given by 4 × 9 - 6 × 7 = -6. 

\begin{bmatrix}
1 & 2 & 3 \\ 
4 & 5 & 6\\ 
7 & 8 & 9
\end{bmatrix}

The cofactor of an element is given by (-1)^{i + j} times the minor of the element, where i is the row number and j is the column number. 

For example, in the same matrix as above, the cofactor of 2 is given by (-1)^{1 + 2} times the minor, i.e, 6. Note the i = 1 and j = 2 for element 2.

Similarly, you can find the minors and cofactors for others.

Hence, the minors and cofactors are the important concepts used to determine the adjoint and hence, the inverse of a matrix.