ABSTRACT
Systems of linear algebraic equations can be solved using the matrix inverse, A-I. Consider the general system of linear algebraic equations:
Ax = b
Multiplying Eq. (1.113) by A-I yields
from which
(1.113)
(1.114)
(1.115)
Thus, when the matrix inverse A-I of the coefficient matrix A is known, the solution vector x is simply the product of the matrix inverse A -I and the right-hand-side vector b. Not all matrices have inverses. Singular matrices, that is, matrices whose determinant is zero, do not have inverses. The corresponding system of equations does not have a unique solution.
