How do you solve using gaussian elimination or gauss-jordan elimination, #2x₁+4x₂-6x₃= 10#, #3x₁+3x₂-3x₃= 6#?

1 Answer
Jan 6, 2018

Answer:

#P=({-1-p, 3+2p, p}, p in RR)#

Explanation:

#([2,4,-6,|,10],[3,3,-3,|,6])~~([6,12,-18,|,30],[6,6,-6,|,12])#
#R_1=R_1xx3#
#R_2=R_2xx2#
#R_2=R_2-R_1#

#([6,12,-18,|,30],[0,-6,12,|,-18])~~([1,2,-3,|,5],[0,1,-2,|,3])#
#R_1=R_1xx1/6#
#R_2=R_2xx-1/6#
#R_1=R_1-2xxR_2#

#([1,0,1,|,-1],[0,1,-2,|,3])#

We have to set #x_3# as parameter #p#:
#x_1=-1-p#
#x_2=3+2p#
#x_3=pcolor(white)(QQQQQQQQQQQ)p in RR#

#P=({-1-p, 3+2p, p}, p in RR)#