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274

Part of 1954 Moscow Mathematical Olympiad

Problems(1)

MMO 274 Moscow MO 1954 7x7 linear system

Source:

8/13/2019
Solve the system {10x1+3x2+4x3+x4+x5=011x2+2x3+2x4+3x5+x6=015x3+4x4+5x5+4x6+x7=02x1+x2−3x3+12x4−3x5+x6+x7=06x1−5x2+3x3−x4+17x5+x6=03x1+2x2−3x3+4x4+x5−16x6+2x7=04x1−8x2+x3+x4+3x5+19x7=0\begin{cases} 10x_1 + 3x_2 + 4x_3 + x_4 + x_5 = 0 \\ 11x_2 + 2x_3 + 2x_4 + 3x_5 + x_6 = 0 \\ 15x_3 + 4x_4 + 5x_5 + 4x_6 + x_7 = 0 \\ 2x_1 + x_2 - 3x_3 + 12x_4 - 3x_5 + x_6 + x_7 = 0 \\ 6x_1 - 5x_2 + 3x_3 - x_4 + 17x_5 + x_6 = 0 \\ 3x_1 + 2x_2 - 3x_3 + 4x_4 + x_5 - 16x_6 + 2x_7 = 0\\ 4x_1 - 8x_2 + x_3 + x_4 + 3x_5 + 19x_7 = 0 \end{cases}
system of equationsalgebra