5. 4 3
Given matrix is,
A = [ 2 − 2 4 3 ]
The determinant of the given matrix is,
| A | = 2 × 3 − ( − 2 ) × 4 = 6 + 8 = 14
Cofactor of a 11 is,
A 11 = ( − 1 ) 1 + 1 ( 3 ) = 3
Cofactor of a 12 is,
A 12 = ( − 1 ) 1 + 2 ( 4 ) = − 4
Cofactor of a 21 is,
A 21 = ( − 1 ) 2 + 1 ( − 2 ) = 2
Cofactor of a 22 is,
A 22 = ( − 1 ) 2 + 2 ( 2 ) = 2
So, the adjoint of the given matrix is,
a d j A = [ A 11 A 21 A 12 A 22 ] = [ 3 2 − 4 2 ]
The inverse of the given matrix is,
A − 1 = 1 | A | a d j A = 1 14 [ 3 2 − 4 2 ]
Given matrix is,
The determinant of the given matrix is,
Cofactor of
Cofactor of
Cofactor of
Cofactor of
So, the adjoint of the given matrix is,
The inverse of the given matrix is,
