# Calculating the singular configuration of a 3 revolute joint manipulator

I would really appreciate it if somebody could help me calculate the singular configuration of this simple manipulator

I am confused since J is a 2x3 matrix and I cannot simply calculate the derivative.

If $J$ is not square, solve $$|J^TJ| = 0$$ for $\theta_i$.
Singular configurations are configurations at which the Jacobian is rank-deficient. In this case $J$ is a square matrix, you can find conditions for singularity by solving $\det(J) = 0$.
The last row of $J$ being all ones means that no matter the configuration, you can always generate some angular velocity. This actually implies that the conditions you get from solving $\det(J) = 0$ will be the conditions for linear velocity singularities.