Solve the system using the gauss-jordan method. 2x – 3y – 9z = 12 4x + 5y – 6z = –14 –5x + 3y – 9z = 21 a. (–3, 7, –5) b. c. no solution d.

Step-by-step explanation:

We are given the equations,

2x - 3y - 9z = 12

4x + 5y - 6z = - 14

-5x + 3y - 9z = 21

Then, the augmented matrix is given by,

Now, we will apply some rules to get the row-echlon form of the matrix.

1. .

This gives,

2. and

We get,

3.

So,

4. and

We get,

5.

We get,

6. and

So,

Thus, we get,

x = -3, y = -2 and z = .

Hence, the solution is .