The given matrix is an augmented matrix used in the solution of a system of linear equations. What is the solution of the system?
A) , ,
B) , ,
C) , ,
D) , ,
E) , ,

Question

The given matrix is an augmented matrix used in the solution of a system of linear equations. What is the solution of the system? 
A) , , 
B) , , 
C) , , 
D) , , 
E) , ,

Quizplus · Accepted Answer

We can use Gaussian elimination to solve the system. First, we start with the augmented matrix:

[3 1 -2 7]
[1 -2 1 -3]
[2 1 2 9]

To eliminate the 2 in the first column, we subtract twice the first row from the third row, giving us:

[3 1 -2 7]
[1 -2 1 -3]
[0 -1 6 -5]

We now use back substitution to solve for x, y and z:

z = (-5/6)
-y + 6z = 5
3x + y - 2z = 7

Substituting z, we get:

-y + 6(-5/6) = 5
y = 10

And substituting y and z, we get:

3x + 10 - 2(-5/6) = 7
3x = 23/2
x = 23/6

Therefore, the solution of the system is (23/6, 10, -5/6), which corresponds to choice D.

The Given Matrix Is an Augmented Matrix Used in the Solution