Question

Consider the system? −3x + 5y + 3z = 0 6x + −7y + −4z = −2 9x + −6y + −3z = −6 Gaussian elimination of the augmented matrix for this system produces the matrix

Consider the system
−3x + 5y + 3z = 0
6x + −7y + −4z = −2
9x + −6y + −3z = −6
Gaussian elimination of the augmented matrix for this system produces the matrix

Answer 1

The solution is `((x),(y),(z))=((-10/9-1/9z),(-2/3-2/3z),(z))`

Explanation:

We perform the Gauss elimination on the augmented matrix

`((-3,5,3,|,0),(6,-7,-4,|,-2),(9,-6,-3,|,-6))`

`R_3larr(R3)/3`,

`((-3,5,3,|,0),(6,-7,-4,|,-2),(3,-2,-1,|,-2))`

and `R_3larrR3+R1`

`((-3,5,3,|,0),(6,-7,-4,|,-2),(0,3,2,|,-2))`

and `R_2larrR2+2R1`

`((-3,5,3,|,0),(0,3,2,|,-2),(0,3,2,|,-2))`

and `R_3larrR3-R2`

`((-3,5,3,|,0),(0,3,2,|,-2),(0,0,0,|,0))`

and `R_2larr(R2)/3`

`((-3,5,3,|,0),(0,1,2/3,|,-2/3),(0,0,0,|,0))`

and `R_1larr(R1)/(-3)`

`((1,-5/3,-1,|,0),(0,1,2/3,|,-2/3),(0,0,0,|,0))`

and `R_1larrR1+5/3R2`

`((1,0,1/9,|,-10/9),(0,1,2/3,|,-2/3),(0,0,0,|,0))`