Solution of Simultaneous Linear Algebraic Equations

Eamiliarity with matrix-vector notation and results involving matrices will be assumed, but most of what is needed is provided in the Appendix A. Detailed derivations will be replaced by clarifying examples, most of which will be borrowed from the literature. These borrowed examples are chosen, because they have already been tested in the context of the algorithm or method under discussion. 

The objective is to determine the values of Xj, X2, and X3 that will simultaneously solve all three equations. In general, the System 9.15 is a subset of the n linear equations in n unknowns represented by 

Linear equations result naturally when we conduct material and energy balances, but most applications occur when we implement other numerical methods. One of the most basic solutirm techniques for systems such as Equation 9.15 is Gaussian elimination [3,5,9,13,14], which is illustrated using the System of Equations 9.15. 

We start by using the coefficient of Xi in the first equation—designated as El, to eliminate the coefficients of Xi in the other equations—designated as Ej and E3, respectively. That is, (—4) times Ei added to E3 produces 

The new equivalent system of equations resulting from the above elementary operation is 

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It has been proposed to represent the TF with 10 CSTR staged units 0.3 ft in length. Develop solutions to this problem using a finite difference method of solving an ordinary differential equation and a lumped parameter model employing a method of solution of simultaneous linear algebraic equations. 

Numerical Solution of Simultaneous Linear Algebraic Equations... 

NumerPcal Solution of Simultaneous Linear Algebraic Equations Chapter 2 Table 2.3 Number of operstlone needed by Cramer s rule... 

The most widely used method for solution of simultaneous linear algebraic equations is the Gauss elimination method. This is based on the principle of converting the set of n equations in n unknowns ... 

Example 2.2 demonstrates the use of the Gauss-Jordan reduction method for the solution of simultaneous linear algebraic equations. 

Gauss Elimination method for solution of simultaneous linear algebraic equations. 

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