Solve Using an Augmented Matrix 2x+3y=11 , 3x+3y=9 , x+y+3z=1

Problem

{[2*x+3*y=11],[3*x+3*y=9],[x+y+3*z=1])

Solution

1. Write the augmented matrix representing the system of linear equations.

[[2,3,0,|,11],[3,3,0,|,9],[1,1,3,|,1]]

2. Swap rows to place a 1 in the first pivot position ((R_1)↔(R_3).

[[1,1,3,|,1],[3,3,0,|,9],[2,3,0,|,11]]

3. Eliminate the first column entries below the pivot by performing (R_2)−3*(R_1)→(R_2) and (R_3)−2*(R_1)→(R_3)

[[1,1,3,|,1],[0,0,−9,|,6],[0,1,−6,|,9]]

4. Swap rows to bring a non-zero value to the second pivot position ((R_2)↔(R_3).

[[1,1,3,|,1],[0,1,−6,|,9],[0,0,−9,|,6]]

5. Scale the third row to create a leading 1 by performing −1/9*(R_3)→(R_3)

[[1,1,3,|,1],[0,1,−6,|,9],[0,0,1,|,−2/3]]

6. Eliminate the third column entries above the pivot by performing (R_2)+6*(R_3)→(R_2) and (R_1)−3*(R_3)→(R_1)

[[1,1,0,|,3],[0,1,0,|,5],[0,0,1,|,−2/3]]

7. Eliminate the second column entry above the pivot by performing (R_1)−(R_2)→(R_1)

[[1,0,0,|,−2],[0,1,0,|,5],[0,0,1,|,−2/3]]

Final Answer

(x,y,z)=(−2,5,−2/3)

Want more problems? Check here!