Relationship between pseudoOuts and Real outputs

Question

For each real input, we have a pseduoOut which is commitment to the same amount as the real input. We can therefore subtract the realInputCommitment from the pseudoOut and prove that it is a commitment to zero by signing for it in a ring signature.

Once I do this for each input, how do I then prove that the sum of inputs is equal to the sum of outputs? If I understood correctly, the pseudoOuts are an intermediate step.

Page49 of zero to monero shows a formula whereby: Sum of PseudoOuts = sumOuts + fees * H

This seems to imply that we must choose the blinding factors in the pseduoOuts in such a way that the sum cancels out with the sum of the blinding factors in the real outputs plus fee*H?

Answer 1

This seems to imply that we must choose the blinding factors in the pseduoOuts in such a way that the sum cancels out with the sum of the blinding factors

And that's what happens. The blinding factors chosen are random numbers [source] for all but the last input. Then the last inputs is calculated so that the sum of all inputs is the same as the sum of the outputs [source].