Determine whether the following equations will have non-trivial solutions, if so solve them: `x+3y-2z=0, 2x-y+4z=0,x-11y+14z=0`

Explanation

To determine whether the given system of equations has non-trivial solutions and to find those solutions, we will follow these steps:

### Step 1: Write the system of equations in matrix form
The given equations are:
1. \( x + 3y - 2z = 0 \)
2. \( 2x - y + 4z = 0 \)
3. \( x - 11y + 14z = 0 \)

...