There is NO solipsism in The Matrix, any quotes or scenes would have to be taken out of context to apply. The Matrix is very Dualistic, that's the whole point. Specifically the ideas in The Matrix are _Platonic Dualism_ and some elements of the _Vedantic "Maya"_ (regarding the description of the illusionary world).
Solipsism is complete skepticism of the exterior, and thinking you are all the exists and everything else is your "imagination." Only the cogito exists, if that.
Dualism is the seperation of the physical and mental worlds, the body and the mind. Platonic Dualism puts "real" existence in the intelligible world of the mind. The physical exterior world is an illusion (similar to the "Maya," although it is not dualistic) inhabited by imperfect shadows of the intelligible ideals.
Dualism still believes in other humans, absolutes, and truths... it's just the true existence is the mind not the physical world. Just like the matrix in the movie. Neo must escape the perceived "physical" world of The Matrix to reach Truth and self-knowledge in the "real" world.
The spoon scene ("Mind over body", "bend yourself") is an example of mind-body dualism. Existence is in the mind, so the mind has control over the physical.
EDIT - Red Pill, blue pill - another example of dualism.