How do you solve the following system?:# 7x+2y-z=3, 8x+3y+5z=9, 8x-8y-2z=4#

1 Answer
Jan 15, 2018

Answer:

The solution is #((x),(y),(z))=((131/219),(-29/219),(202/219))#

Explanation:

Perform the Gauss Jordan elimination on the augmented matrix,

The last equation is first

#A=((8,-8,-2,|,4),(8,3,5,|,9),(7,2,-1,|,3))#

Perform the row operations

Make the first column the pivot , #R1larr(R1)/8#

#((1,-1,-1/4,|,1/2),(8,3,5,|,9),(7,2,-1,|,3))#

Eliminate the first column, #R2larr(R2-8R1)# and #R3larr(R3-7R1)#

#((1,-1,-1/4,|,1/2),(0,11,7,|,5),(0,9,3/4,|,-1/2))#

Make the pivot in the second column, #R2larr(R2)/11#

#((1,-1,-1/4,|,1/2),(0,1,7/11,|,5/11),(0,9,3/4,|,-1/2))#

Eliminate the second column, #R3larr(R3-9R2)#

#((1,-1,-1/4,|,1/2),(0,1,7/11,|,5/11),(0,0,-219/44,|,-101/22))#

Make the pivot in the third column, #R3larr(R3xx-44/219)#

#((1,-1,-1/4,|,1/2),(0,1,7/11,|,5/11),(0,0,1,|,202/219))#

Eliminate the third column, #R2larr R2-7/11R3#

#((1,-1,-1/4,|,1/2),(0,1,0,|,-29/219),(0,0,1,|,202/219))#

#R1larr(R1+R2)# and #R1larrR1+1/4R3#

#((1,0,0,|,131/219),(0,1,0,|,-29/219),(0,0,1,|,202/219))#