Question

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

Answer 1

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))`