# 10th Int'l Conference on Numerical Methods in Fluid Dynamics by Feng Gan Zhuang, You Lan Zhu By Feng Gan Zhuang, You Lan Zhu

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Now Ly = b can be solved for y by forward substitution, followed by the solution of Ux = y by means of back substitution. The equations Ix = c, which are produced by Gauss–Jordan elimination, are equivalent to x = c (recall the identity Ix = x), so that c is already the solution. 37) = 0 Since the determinant is zero, the matrix is singular. It can be veriﬁed that the singularity is due to the following row dependency: (row 3) = (3 × row 1) − (row 2). 2 3 ]T Gauss Elimination Method Introduction Gauss elimination is the most familiar method for solving simultaneous equations.

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Linear Systems Linear, algebraic equations occur in almost all branches of numerical analysis. But their most visible application in engineering is in the analysis of linear systems (any system whose response is proportional to the input is deemed to be linear). , most topics taught in an engineering curriculum. If the system is discrete, such as a truss or an electric circuit, then its analysis leads directly to linear algebraic equations. In the case of a statically determinate truss, for example, the equations arise when the equilibrium conditions of the joints are written down.