Question

In: Math

Solve the following system. If the​ system's equations are dependent or if there is no​ solution,...

Solve the following system. If the​ system's equations are dependent or if there is no​ solution, state this.

3x - 4y -z = 9

2x + 2y + z = 0

5x - 2y + 2z = -1

The solution is....

PLEASE MAKE SURE THIS IS CORRECT. I KEEP PAYING FOR THE WRONG ANSWER!

Solutions

Expert Solution

Augmented matrix for given system of equations

solution using Gauss-Jordan elimination

Your matrix

X1 X2 X3 b
1 3 -4 -1 9
2 2 2 1 0
3 5 -2 2 -1

Make the pivot in the 1st column by dividing the 1st row by 3

X1 X2 X3 b
1 1 -4/3 -1/3 3
2 2 2 1 0
3 5 -2 2 -1

Eliminate the 1st column

X1 X2 X3 b
1 1 -4/3 -1/3 3
2 0 14/3 5/3 -6
3 0 14/3 11/3 -16

Make the pivot in the 2nd column by dividing the 2nd row by 14/3

X1 X2 X3 b
1 1 -4/3 -1/3 3
2 0 1 5/14 -9/7
3 0 14/3 11/3 -16

Eliminate the 2nd column

X1 X2 X3 b
1 1 0 1/7 9/7
2 0 1 5/14 -9/7
3 0 0 2 -10

Make the pivot in the 3rd column by dividing the 3rd row by 2

X1 X2 X3 b
1 1 0 1/7 9/7
2 0 1 5/14 -9/7
3 0 0 1 -5

Eliminate the 3rd column

X1 X2 X3 b
1 1 0 0 2
2 0 1 0 1/2
3 0 0 1 -5

Solution set:

x = 2

y = 1/2

z = -5

The solution is.... (x,y,z) = ( 2 , 1/2 , -5) (Answer)


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