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(B) The augmented matrix is $\begin{bmatrix} 1 & 1 & 1 & 5 \ 1 & 2 & 3 & 9 \ 1 & 3 & \lambda & \mu \end{bmatrix}$.Applying row operations $R_2 	o R

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$18$

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(B) The augmented matrix is $\begin{bmatrix} 1 & 1 & 1 & 5 \ 1 & 2 & 3 & 9 \ 1 & 3 & \lambda & \mu \end{bmatrix}$.Applying row operations $R_2 	o R_2 - R_1$ and $R_3 	o R_3 - R_1$, we get:$\begin{bmatrix} 1 & 1 & 1 & 5 \ 0 & 1 & 2 & 4 \ 0 & 2 & \lambda-1 & \mu-5 \end{bmatrix}$.Now applying $R_3 	o R_3 - 2R_2$, we get:$\begin{bmatrix} 1 & 1 & 1 & 5 \ 0 & 1 & 2 & 4 \ 0 & 0 & \lambda-5 & \mu-13 \end{bmatrix}$.For the system to have infinitely many solutions, the rank of the coefficient matrix must be equal to the rank of the augmented matrix and must be less than the number of variables. This requires the last row to be a zero row:$\lambda - 5 = 0 \Rightarrow \lambda = 5$.$\mu - 13 = 0 \Rightarrow \mu = 13$.Therefore, $\lambda + \mu = 5 + 13 = 18$.

If the system of equations $x + y + z = 5$, $x + 2y + 3z = 9$, $x + 3y + \lambda z = \mu$ has infinitely many solutions, then the value of $\lambda + \mu$ is:

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