Using Cofactors of elements of second row, evaluate .
Given determinant is,
| 5 3 8 2 0 1 1 2 3 |
Minor of a 21 is,
M 21 = | 3 8 2 3 | = 9 − 16 = − 7
Minor of a 22 is,
M 22 = | 5 8 1 3 | = 15 − 8 = 7
Minor of a 23 is,
M 23 = | 5 3 1 2 | = 10 − 3 = 7
Cofactor of a 21 is,
A 21 = ( − 1 ) 2 + 1 ( − 7 ) = 7
Cofactor of a 22 is,
A 22 = ( − 1 ) 2 + 2 ( 7 ) = 7
Cofactor of a 23 is,
A 23 = ( − 1 ) 2 + 3 ( 7 ) = − 7
The value of the given determinant is,
Δ = a 21 A 21 + a 22 A 22 + a 23 A 23 = 2 × 7 + 0 × 7 + 1 × ( − 7 ) = 14 − 7 = 7
Given determinant is,
Minor of
Minor of
Minor of
Cofactor of
Cofactor of
Cofactor of
The value of the given determinant is,
.