Solve the system of linear equations using the Gauss-Jordan elimination method.

Question

Quizplus · Accepted Answer

Using Gauss-Jordan elimination method, the augmented matrix of the system can be written as:

[2 1 1 | 11]
[4 5 3 | 32]
[6 7 5 | 53]

R2 - 2R1 -> R2:
[2 1 1 | 11]
[0 3 1 | 10]
[6 7 5 | 53]

R3 - 3R1 -> R3:
[2 1 1 | 11]
[0 3 1 | 10]
[0 4 2 | 20]

R3 - (4/3)R2 -> R3:
[2 1 1 | 11]
[0 3 1 | 10]
[0 0 2/3 | 2/3]

Multiplying R3 by 3/2:
[2 1 1 | 11]
[0 3 1 | 10]
[0 0 1 | 1]

R2 - R3 -> R2:
[2 1 1 | 11]
[0 3 0 | 9]
[0 0 1 | 1]

R1 - R3 -> R1:
[2 1 0 | 10]
[0 3 0 | 9]
[0 0 1 | 1]

R1 - R2 -> R1:
[2 0 0 | 1]
[0 3 0 | 9]
[0 0 1 | 1]

Dividing R1 by 2 and R2 by 3:
[1 0 0 | 1/2]
[0 1 0 | 3]
[0 0 1 | 1]

Therefore, the solution is:
a = 1/2, b = 3, e = 1.
The corresponding answer is C.

Solve the System of Linear Equations Using the Gauss-Jordan Elimination