Final answer:
To solve the given system of equations as a matrix equation and use inverses to find the solution for X, we need to represent the equations as a coefficient matrix, variable matrix, and constant matrix. Then, we can multiply both sides of the equation by the inverse of the coefficient matrix to isolate X.
Step-by-step explanation:
To write the given system of equations as a matrix equation, we can represent the coefficients of the variables as a matrix, the variables as a column matrix, and the constants as another column matrix. The matrix equation can then be written as:
AX = B
where A is the coefficient matrix, X is the variable matrix, and B is the constant matrix.
To solve the system using inverses, we can multiply both sides of the equation by the inverse of matrix A:
A-1AX = A-1B
Simplifying, we get:
X = A-1B
Substituting the given values into the equation and using matrix inverses, we can find the solution for X.