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Solve the system of equations [ILL 1974]

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January 2, 2011
parameterizationalgebra proposedalgebra

Problem Statement

Solve the following system of linear equations with unknown x1,x2…,xn (n≥2)x_1,x_2 \ldots, x_n \ (n \geq 2) and parameters c1,c2,…,cn:c_1,c_2, \ldots , c_n:
2x1−x2=c1;2x_1 -x_2 = c_1;−x1+2x2−x3=c2;-x_1 +2x_2 -x_3 = c_2;−x2+2x3−x4=c3;-x_2 +2x_3 -x_4 = c_3;⋯⋯⋯\cdots \qquad \cdots \qquad \cdots \qquad−xn−2+2xn−1−xn=cn−1;-x_{n-2} +2x_{n-1} -x_n = c_{n-1};−xn−1+2xn=cn.-x_{n-1} +2x_n = c_n.
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