Procedural languages equation solving

The direct solution of equation (4 18) or (4 22) is in the MCSCF language called a one-step procedure, since both S and T are updated simultaneously. We can formally rewrite (4 16) (or (4 22)) as a two-step procedure by solving for S first. From the first row of (4 16) we obtain ... 

The solution is represented by a column vector that is equal to the matrix product A C. In order for a matrix to possess an inverse, it must be nonsingular, which means that its determinant does not vanish. If the matrix is singular, the system of equations cannot be solved because it is either linearly independent or inconsistent. We have already discussed the inversion of a matrix in Chapter 9. The difficulty with carrying out this procedure by hand is that it is probably more work to invert an n by n matrix than to solve the set of equations by other means. However, with access to Mathematica, BASIC, or another computer language that automatically inverts matrices, you can solve such a set of equations very quickly. 

A major portion of solving a problem by computer is in block diagraming. A block diagram is an outline or flow chart of the problem. From this diagram and the necessary equations, a step by step procedure can be written that the computer can follow (this is a program). This procedure is written in the language of the computer at hand. 

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