If the system of linear equations
x+ y +z = 5
x+2y +2z = 6
`x + 3y + lambdaz = mu, (lambda, mu in R)` has infinitely many solutions, then the value of `lambda + mu` is

Options

A. 7
B. 12
C. 10
D. 9

Explanation

To solve the given system of linear equations for the values of \( \lambda \) and \( \mu \) such that the system has infinitely many solutions, we will follow these steps:

1. **Write the system of equations in matrix form**:
The system of equations can be represented as:
\[
\begin{bmatrix}
1 & 1 & 1 \\
1 & 2 & 2 \\
...