= Solution
At each transition, choose a coordinate uniformly and independently of the previous coordinate choices. Draw a fresh value from that coordinate's <full conditional distribution> given the current remaining coordinates, and keep all other coordinates fixed. This supplies the random-selection and conditional-draw operations lost in the TeX transcription. The update depends only on the current vector and fresh randomness, which proves the <Markov property>. The printed mathematical requests are the kernel and its <detailed balance>, answered in the following two subsections.
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