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National and Regional Contests
Russia Contests
Moscow Mathematical Olympiad
1954 Moscow Mathematical Olympiad
274
MMO 274 Moscow MO 1954 7x7 linear system
MMO 274 Moscow MO 1954 7x7 linear system
Source:
August 13, 2019
system of equations
algebra
Problem Statement
Solve the system
{
10
x
1
+
3
x
2
+
4
x
3
+
x
4
+
x
5
=
0
11
x
2
+
2
x
3
+
2
x
4
+
3
x
5
+
x
6
=
0
15
x
3
+
4
x
4
+
5
x
5
+
4
x
6
+
x
7
=
0
2
x
1
+
x
2
−
3
x
3
+
12
x
4
−
3
x
5
+
x
6
+
x
7
=
0
6
x
1
−
5
x
2
+
3
x
3
−
x
4
+
17
x
5
+
x
6
=
0
3
x
1
+
2
x
2
−
3
x
3
+
4
x
4
+
x
5
−
16
x
6
+
2
x
7
=
0
4
x
1
−
8
x
2
+
x
3
+
x
4
+
3
x
5
+
19
x
7
=
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}
⎩
⎨
⎧
10
x
1
+
3
x
2
+
4
x
3
+
x
4
+
x
5
=
0
11
x
2
+
2
x
3
+
2
x
4
+
3
x
5
+
x
6
=
0
15
x
3
+
4
x
4
+
5
x
5
+
4
x
6
+
x
7
=
0
2
x
1
+
x
2
−
3
x
3
+
12
x
4
−
3
x
5
+
x
6
+
x
7
=
0
6
x
1
−
5
x
2
+
3
x
3
−
x
4
+
17
x
5
+
x
6
=
0
3
x
1
+
2
x
2
−
3
x
3
+
4
x
4
+
x
5
−
16
x
6
+
2
x
7
=
0
4
x
1
−
8
x
2
+
x
3
+
x
4
+
3
x
5
+
19
x
7
=
0
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