(Solution) - At this point the same is only an intuition but -(2025 Original AI-Free Solution)

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At this point "the same" is only an intuition, but nonetheless for each vector space identify the k for which the space is "the same" as Rk.
(a) The 2 × 3 matrices under the usual operations
(b) The n × m matrices (under their usual operations)
(c) This set of 2 × 2 matrices