How do you solve using gaussian elimination or gauss-jordan elimination, #10x-7y+3z+5u=6#, #-6x+8y-z-4u=5#, #3x+y+4z+11u=2#, #5x-9y-2z+4u=7#?

1 Answer
Jan 7, 2018

Answer:

#x=(22+7xx(44/19))/10=3.8210526315789473684210526315789#

#y=44/19=2.3157894736842105263157894736842#

#z=-7#

#u=1#

Explanation:

#([10,-7,3,5,|,6],[-6,8,-1,-4,|,5],[3,1,4,11,|,2],[5,-9,-2,4,|,7])~~([10,-7,3,5,|,6],[-6,8,-1,-4,|,5],[6,2,8,22,|,4],[10,-18,-4,8,|,14])#
#R_4=R_4xx2#
#R_3=R_3xx2#
#R_4=R_4-R_1#
#R_3=R_3+R_2#

#([10,-7,3,5,|,6],[-6,8,-1,-4,|,5],[0,10,7,18,|,9],[0,-11,-7,3,|,8])~~([30,-21,9,15,|,18],[-30,40,-5,-20,|,25],[0,10,7,18,|,9],[0,-11,-7,3,|,8])#
#R_1=R_1xx3#
#R_2=R_2xx5#
#R_2=R_2+R_1#

#([30,-21,9,15,|,18],[0,19,4,-5,|,43],[0,10,7,18,|,9],[0,-11,-7,3,|,8])~~([30,-21,9,15,|,18],[0,19,4,-5,|,43],[0,10,7,18,|,9],[0,-110,-70,30,|,80])#
#R_4=R_4*10#
#R_4=R_4+11xxR_3#

#([30,-21,9,15,|,18],[0,19,4,-5,|,43],[0,10,7,18,|,9],[0,0,7,228,|,179])~~([30,-21,9,15,|,18],[0,190,40,-50,|,430],[0,190,133,342,|,171],[0,0,7,228,|,179])#
#R_3=R_3xx19#
#R_2=R_2xx10#
#R_3=R_3-R_2#

#([30,-21,9,15,|,18],[0,190,40,-50,|,430],[0,0,93,392,|,-259],[0,0,7,228,|,179])~~([30,-21,9,15,|,18],[0,190,40,-50,|,430],[0,0,651,2744,|,-1813],[0,0,651,21204,|,16647])#
#R_4=R_4xx93#
#R_3=R_3xx7#
#R_4=R_4-R_3#

#([30,-21,9,15,|,18],[0,190,40,-50,|,430],[0,0,651,2744,|,-1813],[0,0,0,18460,|,18460])~~([10,-7,3,5,|,6],[0,19,4,-5,|,43],[0,0,93,392,|,-259],[0,0,0,1,|,1])#
Dividing what is possible
#R_3=R_3-392xxR_4#
#R_2=R_2+5xxR_4#
#R_2=R_2-5xxR_4#

#([10,-7,3,0,|,1],[0,19,4,0,|,48],[0,0,93,0,|,-651],[0,0,0,1,|,1])~~([10,-7,0,0,|,22],[0,19,0,0,|,44],[0,0,1,0,|,-7],[0,0,0,1,|,1])#
#R_3=R_3xx1/93#
#R_2=R_2-4xxR_3#
#R_1=R_1-3xxR_3#
#R_2=R_2xx1/19#
#R_1=R_1+7xxR_2#

#([1,0,0,0,|,(22+7xx(44/19))/10],[0,1,0,0,|,44/19],[0,0,1,0,|,-7],[0,0,0,1,|,1])#

#x=(22+7xx(44/19))/10=3.8210526315789473684210526315789#

#y=44/19=2.3157894736842105263157894736842#

#z=-7#

#u=1#