Final answer:
To solve the given system of equations by inverting the coefficient matrix, we would first express it in matrix form, find the inverse of the coefficient matrix, and then multiply it by the constants matrix to obtain the solution.
Step-by-step explanation:
To solve the system of equations by inverting the coefficient matrix, we first need to write the equations in matrix form. The system provided in the question seems to have some typographical errors. Assuming the correct system of equations is:
1x1 + x2 = 2
5x1 + 6x2 = 9
We can then form the coefficient matrix A and the constant matrix B:
A = [[1, 1], [5, 6]]
B = [[2], [9]]
The next step is to find the inverse of matrix A, which we'll call A-1. After that, we multiply the inverse A-1 by matrix B to find the solution matrix X:
X = A-1B
Computing A-1 can be done using the formula for a 2x2 matrix:
A-1 = (1/det(A)) * adj(A)
where det(A) is the determinant of A and adj(A) is the adjugate of A. Finally, we compute the product of A-1 and B to find the values of x1 and x2, which are the solutions to the system of equations.