When combining a revolute joint and an angle constraint to form the 2x2 block K matrix consisting of four 3x3 matrices below for an elbow joint with restricted angular movement, how do I invert this matrix to solve for lambda, which seems like another matrix of two 3x1 vectors as follows:
In 2D a revolute joint with one limit would result in a 3x3 matrix. If you have N constraints the dimension of the effective mass matrix is N x N. If this isn't your result you made a mistake.
Also note that since you mention a limit you would need to solve a LCP and not a linear system (e.g. using direct enumeration). You can find an example how to solve these kinds of problems in Box2D.