Final answer:
To solve the given system of equations using an inverse matrix, express the system in matrix form, compute the inverse of the coefficient matrix, and multiply it by the constants matrix to find the variables' values.
Step-by-step explanation:
To solve the system of linear equations x + 2y = 8 and x - 2y = 0 using an inverse matrix, we first need to write the system in matrix form as AX = B, where A is the coefficient matrix, X is the column matrix of variables, and B is the column matrix of constants. In this case, A = [[1, 2], [1, -2]], X = [[x], [y]], and B = [[8], [0]].
We then calculate the inverse of matrix A, which we'll denote as A⁻¹. If A⁻¹ exists, we can then solve for X by multiplying both sides of the matrix equation by A⁻¹, yielding X = A⁻¹B. The solution of the system of equations will be the elements of matrix X.
After calculating A⁻¹ and performing the matrix multiplication with B, we obtain the specific values of x and y that satisfy both equations, thus solving the system. Remember to check that A⁻¹ exists, as without it, this method cannot be used to solve the system.