Can the adj(A) method be simplified for finding inverses of 4x4 matrices?

[delgeezee]

I can find inverses using an adjust for a 3X3 matrix. But My homework book asks us to find the inverse using an adj(A) for a 4x4 matrix. 1 3 1 1
2 5 2 2
1 3 8 9
1 3 2 2

it seems less time efficient to find the inverse using this method. Is it possible to reduce the matrix to a a simpler yet equal form and still come out with the same cofactor matrix?

 

[Opalg]

I can find inverses using an adjust for a 3X3 matrix. But My homework book asks us to find the inverse using an adj(A) for a 4x4 matrix. 1 3 1 1
2 5 2 2
1 3 8 9
1 3 2 2

it seems less time efficient to find the inverse using this method. Is it possible to reduce the matrix to a a simpler yet equal form and still come out with the same cofactor matrix?

Even for a 3x3 matrix, the adjoint method is a very laborious way to find the inverse. For anything larger than that, it rapidly gets far worse. Maybe the purpose of this exercise in the homework book is to get you to see how bad the adjoint method is, so that you will appreciate the value of having other methods.

 

[Jameson]

I agree completely that finding the $\text{adj A}$ is very tedious and there isn't any way to simplify the process (row reduction for example will result in a different answer). You will have to calculate 16 determinants for matrices of size 3x3 in this problem. Not fun!