Answer:
The inverse of the matrix A is:
A^-1 = [[-1/7 10/49 -6/49] , [-18/49 -3/49 22/147] , [5/7 -2/49 -1/49]]
Step-by-step explanation:
To find the inverse of matrix A, we need to follow the following steps:
Step 1: Calculate the determinant of matrix A
det(A) = |-3 -2 2|
| 1 3 1|
| 4 4 -1|
= -3(3(-1) - 4(1)) - 2(1(-1) - 4(2)) + 2(1(4) - 3(4)
= -7
Step 2: Find the adjugate of A, which is the transpose of the matrix of cofactors of A
Adj(A) = [Cof(A)]^T
Cof(A) = [[ 7 18 -10] , [-10 -11 10] , [ 4 14 -7]]
Adj(A) = [[ 7 -10 4] , [18 -11 14] , [-10 10 -7]]
Step 3: Compute the inverse of A using the formula:
A^-1 = (1/det(A)) * Adj(A)
A^-1 = (1/-7) * [[ 7 -10 4] , [18 -11 14] , [-10 10 -7]]
A^-1 = [[-1/7 10/49 -6/49] , [-18/49 -3/49 22/147] , [5/7 -2/49 -1/49]]
Therefore, the inverse of matrix A is:
A^-1 = [[-1/7 10/49 -6/49] , [-18/49 -3/49 22/147] , [5/7 -2/49 -1/49]]
Hope this helped, sorry if it didn't. If you need more help, ask me! :]