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4x4 system, x_1 + ax_2 + x_3 = b

Source: 1967-68 Germany R4 12.1

October 13, 2024
algebrasystem of equationsSystem

Problem Statement

Determine all ordered quadruples of real numbers (x1,x2,x3,x4)(x_1, x_2, x_3, x_4) for which the following system of equations exists, is fulfilled: x1+ax2+x3=bx_1 + ax_2 + x_3 = b x2+ax3+x4=bx_2 + ax_3 + x_4 = b x3+ax4+x1=bx_3 + ax_4 + x_1 = b x4+ax1+x2=bx_4 + ax_1 + x_2 = b Here aa and bb are real numbers (case distinction!).
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