Question

The solution of the following system of linear equations
\(4x_1 - 8x_2 - 2x_3 = 0\)
\(3x_1 - 5x_2 - 2x_3 = 0\) 
\(2x_1 - 8x_2 + x_3 = 0\) is:

• A. \(x_1 = 1, x_2 = 1, x_3 = 1\)
• B. \(x_1 = \frac{3}{2}, x_2 = \frac{1}{2}, x_3 = 0\)
• C. the system has no solution
• D. The system has infinitely many solutions

Hint:

When solving a system with more variables than equations, check if the system is consistent or under-determined. If it is, expect infinitely many solutions

Answer 1

The Correct Option is D

We use Gaussian elimination to solve the system of linear equations. The augmented matrix for this system leads to an under-determined system, indicating infinitely many solutions. This system has dependent equations, meaning we have more variables than independent equations