Which of the following is the formula for cofactor of an element aij ?

1.	Which of the following is the formula for cofactor of an element aij ?
A.	Aij=(1)i+j Mij
B.	Aij=(-2)i+j Mij
C.	Aij=(-1)i+j Mij
D.	Aij=(-1)i-j Mij
Answer» D.

Discussion

For which of the following element in the determinant Δ=\(\begin{vmatrix}5&-5&8\\6&2&-1\\5&-6&8\end{vmatrix}\) , the minor and the cofactor both are zero.
For which of the following elements in the determinant Δ=\(\begin{vmatrix}2&8\\4&7\end{vmatrix}\), the minor of the element is 2?
For which of the elements in the determinant Δ=\(\begin{vmatrix}1&8&-6\\2&-3&4\\-7&9&5\end{vmatrix}\) the cofactor is -37.
Find the minor of the element 2 in the determinant Δ=\(\begin{vmatrix}1&9\\2&3\end{vmatrix}\)?
If Δ=\(\begin{vmatrix}a_{11}&a_{12}&a_{13}\\a_{21}&a_{22}&a_{23}\\a_{31}&a_{32}&a_{33} \end{vmatrix}\), then the determinant in terms of cofactors Aij can be expressed as a11 A11+a21 A21+a31 A31.
Find the cofactor of element -3 in the determinant Δ=\(\begin{vmatrix}1&4&4\\-3&5&9\\2&1&2\end{vmatrix}\).
Find the minor of the element 1 in the determinant Δ=\(\begin{vmatrix}1&5\\3&8\end{vmatrix}\).
Find the minor and cofactor respectively for the element 3 in the determinant Δ=\(\begin{vmatrix}1&5\\3&6\end{vmatrix}\).
What is the minor of the element 5 in the determinant Δ=\(\begin{vmatrix}1&5&4\\2&3&6\\7&9&4\end{vmatrix}\)?
Which of the following is the formula for cofactor of an element aij ?