Question 5154
user Cramer's rule --> but that will involve you calculating 4x4 determinants, so you may decide to ignore that method :-)


Gaussian elimination... here goes :-(


{{{matrix (5, 4, 
 1,  -5,  0, 10,  27,
 5, -25, 10, -4, -47,
10,   2, -1,  4,  36,
 2,   4, -2,  0,  12)
}}}


{{{matrix (5, 4, 
 1,  -5,  0,  10,   27,
 0,   0, 10, -54, -182,
 0,  52, -1, -96, -234,
 0,  14, -2, -20,  -42)
}}}


re-arrnage the rows to move the zero further down and get the smallest number (the 14) in the correct place


{{{matrix (5, 4, 
 1,  -5,  0,  10,   27,
 0,  14, -2, -20,  -42,
 0,   0, 10, -54, -182,
 0,  52, -1, -96, -234)
}}}


divide second by 14 to get a 1


{{{matrix (5, 4, 
 1,  -5,  0,  10,   27,
 0,   1, -1/7, -10/7,  -3,
 0,   0, 10, -54, -182,
 0,  52, -1, -96, -234)
}}}


{{{matrix (5, 4, 
 1, -5,    0,     10,   27,
 0,  1, -1/7,  -10/7,   -3,
 0,  0,   10,    -54, -182,
 0,  0, 45/7, -152/7,  -78)
}}}


divide by 10 to get a 1


{{{matrix (5, 4, 
 1, -5,    0,     10,   27,
 0,  1, -1/7,  -10/7,   -3,
 0,  0,    1,    -27/5, -91/5,
 0,  0, 45/7, -152/7,  -78)
}}}


{{{matrix (5, 4, 
 1, -5,    0,     10,   27,
 0,  1, -1/7,  -10/7,   -3,
 0,  0,    1,    -27/5, -91/5,
 0,  0,    0,     13,  39)
}}}


so, 13w = 39 --> w=3

z - 81/5 = -91/5 --> z = -2

y + 2/7 - 30/7 = -3 --> y = 1

x - 5 + 30 = 27 --> x = 2


THEN IMPORTANTLY, you need to put these 4 answers into each of the original 4 equations to check...check with the 4th one first --> if that works, then odds on you are correct.


PS i hate Gaussian Elimination!


jon