The system of equations: `x+y+z=5` `x+2y+3z=9` `x+3y+lambdaz=mu` has a unique solution, if `lambda=5,mu=13` (b) `lambda!=5` `lambda=5,mu!=13` (d) `mu!=13`

Explanation

To determine the conditions under which the system of equations has a unique solution, we will analyze the given equations step by step.

### Given System of Equations:
1. \( x + y + z = 5 \) (Equation 1)
2. \( x + 2y + 3z = 9 \) (Equation 2)
3. \( x + 3y + \lambda z = \mu \) (Equation 3)

### Step 1: Write the system in matrix form
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