Final answer:
To solve the given system of equations using the matrix inverse method, represent the system in matrix form, find the inverse of matrix A, and solve for X.
Step-by-step explanation:
To solve the given system of equations using the matrix inverse method, we need to represent the system in matrix form. The coefficient matrix is A and the variable matrix is X. The augmented matrix can be written as [A|X].
By using the matrix inverse method, we have [A|X]=[I|A^-1*X], where I is the identity matrix and A^-1 is the inverse of matrix A. So, we need to find the inverse of matrix A which is given by A^-1 = (1/det(A)) * adj(A), where det(A) is the determinant of matrix A and adj(A) is the adjugate of matrix A.
Once we have the inverse of matrix A, we can solve for X by multiplying both sides of [A|X]=[I|A^-1*X] by A^-1.