A First Course in Linear Algebra · Problem T05

Determinants — Robert Beezer

Mathematics — Linear Algebra · dimension-subspaces

Problem

Trivially, if UU and VV are two subspaces of WW with U=VU = V, then dim⁡(U)=dim⁡(V)\dim(U) = \dim(V). Combine this fact, Theorem PSSD, and Theorem EDYES all into one grand combined theorem. You might look to Theorem PIP for stylistic inspiration. (Notice this problem does not ask you to prove anything. It just asks you to roll up three theorems into one compact, logically equivalent statement.)

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