Respuesta :
Answer:
For matrix D=[d11 0 0 ....... 0
0 d22 0 ...... 0
0 0 d33 0 0 ....0
.
.
0 0 0 0 0 . . . dnn]
Adj D =[d22d33..dnn 0 0 0 ....0
0 allvaluesexceptd22 0 0 ...0
0 0 allvaluesexpectd33
.
.
..........allvaluesexceptdnn]
|D|=d11d22d33....dnn
So D-1 = Adj D/|D|
So dividing we get:
D-1=[1/d11 0 0 .... 0
0 0 1/d22 ...0
0 0 0 ......1/dnn]
Step-by-step explanation:
as we know that D-1=AdjD/|D|
and for adj more than 2cross2 we use cofactor method
to find cofactors of matrix we can get
leaving first row and first col
D11=d22d33d44...dnn (as its a diagonal matrix and determinant can be found by multiplying diagonal values)
D12=0 same as all upto D1n=0
D21=0 D22=d11d33d44...dnn all other D22 to D2n=0
and upto so on we can get cofactor matrix as :
[d22d33..dnn 0 0 0 ....0
0 allvaluesexceptd22 0 0 ...0
0 0 allvaluesexpectd33
.
.
..........allvaluesexceptdnn]
Adj D is transpose of cofactor matrix which comes out to be the same :
[d22d33..dnn 0 0 0 ....0
0 allvaluesexceptd22 0 0 ...0
0 0 allvaluesexpectd33
.
.
..........allvaluesexceptdnn]
Now comes determinant:
determinant of diagonal matrix can be calculated by multiplying all diagonal elements
So
|D|=d11d22d33d44...dnn
Solving for D-1 we get :
AdjD/|D|=[1/d11 0 0 .... 0
0 0 1/d22 ...0
0 0 0 ......1/dnn]
