Final answer:
To find the inverse of a matrix, calculate its determinant and check if it is non-zero. If so, use the formula A^-1 = (1/det(A)) * adj(A) to find the inverse.
Step-by-step explanation:
To find the inverse of a matrix, we need to perform a series of steps. First, we check if the matrix is invertible by calculating its determinant. If the determinant is equal to zero, the matrix does not have an inverse. If the determinant is non-zero, we proceed to find the inverse by using the formula:
A-1 = (1/det(A)) * adj(A)
In this case, the given matrix has a non-zero determinant, so we can continue to find its inverse:
Determinant = (-2)(-1)(-9)(17) - (-2)(2)(-1)(4) + (3)(-1)(3)(4) + (3)(2)(3)(4) = 30
Therefore, the inverse of the matrix is:
[17 -1 0 -1] [-4 1 1 -1] [-4 1 3 -1] [-4 1 1 -1]