Dengan determinan
x + 2y = -4
2x + z = 5
y - 3z = - 6
matrik koefisien
[tex]\left[\begin{array}{ccc}1&2&0\\2&0&1\\0&1&-3\end{array}\right] \left[\begin{array}{ccc}x\\y\\z\end{array}\right] = \left[\begin{array}{ccc}-4\\5\\-6\end{array}\right][/tex]
[tex]\rm Det ~D = \left|\begin{array}{ccc}1&2&0\\2&0&1\\0&1&-3\end{array}\right|=[/tex]
[tex]\rm Det~ D = 1(0-1) -2(-6-0) + 0(2-0)[/tex]
det D = -1 + 12 + 0
der D = 11
[tex]\rm Det ~D_x = \left|\begin{array}{ccc}-4&2&0\\5&0&1\\-6&1&-3\end{array}\right|=[/tex]
det Dx = -4(0-1) - 5(-6-0) - 6(2-0)
det Dx = 4 + 30 -12 =
Det Dx = 22
[tex]\rm Det ~D_y = \left|\begin{array}{ccc}1&-4&0\\2&5&1\\0&-6&-3\end{array}\right|=[/tex]
det Dy = 1 (-15 + 6) - 2 (12 + 0) + 0( -4 - 0)
det Dy = - 9 - 24
det Dy = - 33
[tex]\rm Det ~D_z = \left|\begin{array}{ccc}1&2&-4\\2&0&5\\0&1&-6\end{array}\right|=[/tex]
det Dz = 1 (0 - 5) - 2 (-12 + 4) + 0(10-0)
det Dz = -5 + 16
det Dz = 11
x = Dx/D = 22/11 = 2
y = Dy/D = -33/11 = - 3
z= Dz/D = 11/11 = 1
