Příklady z Algebry I: Soustavy lineárních rovnic
(1)
x + 7y -2x - 9y
(2)
3z — 5w 2z + w
x~2y + z   = 0 (3) 2y-8z   = 8
-4a; + 5y + 9z   = -9
(4)
(5)
(6)
(7)
(8)
x + 2y - 3z + u = 7 —x + y — z + u   = 4
x + y — z — u   = 0 x + z — u = 2x + 2y + z - 3-u   = 2
x + y + 2z   = 4 x — y — z   =   —1 2x — 4 y — 5 z   = 1
x+y+z+u   = 0 2x + 2y + z + u   = 0 x + y - z + u   = 0
2x ~ y + 3z   = 0 4x + 2y + 2z   = 0 -2x + 5y - 42   = 0
(9)
(10)
(11)
x + 3y — 13z =
2x - y + 3z = 3
3x + y — 5z = 0
Ax - y + z = 3
x — 2y + z — u =
2x — y + z + u =
3x — 3y + 2z =
x + y + z + u =
x + y + z = 6
x + y - z = 0
x — y + z = 2
2x + 2y + z = 9
-6
(12)
(13)
(14)
x - y + 2z + 3u = 10
x - 2y + 3z + Au + 2v = -2
x + 2y — z — v = —3
2x + 3y — z + u — 2v = —5
x — 2y + z — u   = —1 x — 2y + z + 5u   = 5 x — 2y + z + u   = 1
x + 2y + 5z - 4m = 1
x + 3y + 2z-2u + v = -1
x — 2y + z — u — v = 3
x — 4y + z + u — v = 3
x — 2y + z — u + v = — 1