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

By performing row operations on the augmented matrix, we can reduce it to row echelon form or reduced row echelon form to obtain the solution. The steps of row operations are as follows:

1. Replace R2 with R2-2R1
2. Replace R3 with R3-3R1
3. Replace R4 with R4-R1
4. Replace R3 with R3-2R2
5. Replace R4 with R4+R2
6. Replace R4 with R4-2R3

After performing these operations, the augmented matrix becomes:

[1 2 -3 4 | 5]
[0 1 -1 1 | 1]
[0 0 1 -1 | -2]
[0 0 0 1 | 2]

From this form, we can read off the solution directly as:

x1 = 2
x2 = 1
x3 = -2
x4 = 2

Therefore, the best choice is B.

Use Row Operations on the Augmented Matrix to Solve the Given