A system of linear equations and a reduced matrix for the system are given. Use the reduced matrix to find the general solution of the
System, if one exists.
A) , , for any real number z.
B) , , for any real number z.
C) , , for any real number z.
D) , , for any real number z.
E) no solution

Question

A system of linear equations and a reduced matrix for the system are given. Use the reduced matrix to find the general solution of the ​
System, if one exists.   ​
A) ​, , for any real number z. 
B) ​ , , for any real number z. 
C) ​ , , for any real number z. 
D) ​ , , for any real number z. 
E) ​no solution

Quizplus · Accepted Answer

The reduced matrix is already in row echelon form. Therefore, we can read off the system of equations and their solutions:

- x + 3y − z = 2 ⟹ x = 2 − 3y + z 
- 2y + 3z = 1 ⟹ y = 1/2 − (3/2)z

So, the general solution is given by:

x = 2 − 3y + z = 2 - 3(1/2 - (3/2)z) + z = -5/2z + 5/2 
y = 1/2 − (3/2)z 
z = z

Therefore, the general solution is (−5/2z + 5/2, 1/2 − (3/2)z, z) for any real number z.

A System of Linear Equations and a Reduced Matrix for the System