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# Appendix_SA - Appendix SA SA.1 Solution of Linear...

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1 Appendix SA Solution of Linear Simultaneous Equations SA.1 System of Linear Simultaneous Equations A system of n linear simultaneous equations may be written in the standard form as follows: a 11 x 1 + a 12 x 2 + a 13 x 3 + + a 1 n x n = B 1 a 21 x 1 + a 22 x 2 + a 23 x 3 + + a 2 n x n = B 2 a 31 x 1 + a 32 x 2 + a 33 x 3 + + a 3 n x n = B 3 a n1 x 1 + a n2 x 2 + a n3 x 3 + + a nn x n = B n (SA.1.1) where x 1 , x 2 , , x n are the unknowns, or dependent variables, whose values are to be determined in terms of the B ’s and the a ij coefficients. These coefficients, which in general could be complex numbers, may be ordered in an n × n array as follows: nn n n n n n a a a a a a a a a a a a 3 2 1 2 23 22 21 1 13 12 11 = Δ (SA.1.2) where the i and j subscripts in a ij denote, respectively, the i th row and j th column in the array. The array (SA.1.2) is known as the determinant of the set of simultaneous equations and is denoted by the symbol Δ . The determinant is a number whose value is evaluated according to certain rules.

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