Use row operations on the augmented matrix to solve the given system of linear equations.
A) , ,
B) , ,
C) , ,
D) , ,
E) , ,

Question

Use row operations on the augmented matrix to solve the given system of linear equations. ​  ​
A) , , 
B) , , 
C) , , 
D) , , 
E) , ,

Quizplus · Accepted Answer

Using row operations (add -3 times row 1 to row 2 and add -2 times row 1 to row 3), we can obtain the following reduced row echelon form:

[1, -3, 3, -5]
[0, 7, -5, 13]
[0, 3, -5, 13]

Converting back to equations, we have:

x - 3y + 3z = -5
7y - 5z = 13
3y - 5z = 13

Solving for y and z in terms of x, we get:

y = (5x - 28) / 7
z = (13 - 3y) / 5

Therefore, the solution is given by:

x = t (free variable)
y = (5t - 28) / 7
z = (39 - 15t) / 35

This corresponds to choice C.

Use Row Operations on the Augmented Matrix to Solve the Given