In eukaryotic cells the pyruvate decarboxylation occurs inside the mitochondrial matrix, after transport of the substrate, pyruvate, from the cytosol. The transport of pyruvate into the mitochondria is via the transport protein pyruvate translocase.  Pyruvate translocase transports pyruvate in a symport fashion with a proton (across the inner mitochondrial membrane), which may be considered to be a form of secondary active transport, but further confirmation/support may be needed for the usage of "secondary active transport" desciptor here (Note: the pyruvate transportation method via the pyruvate translocase appears to be coupled to a proton gradient according to S. Papa et al., 1971, seemingly matching secondary active transport in definition).
Alternative sources say "transport of pyruvate across the outer mitochondrial membrane appears to be easily accomplished via large non-selective channels such as voltage-dependent anion channels, which enable passive diffusion" and transport across inner mitochondrial membrane is mediated by mitochondrial pyruvate carrier 1 (MPC1) and mitochondrial pyruvate carrier 2 (MPC2).
Upon entry into the mitochondrial matrix, the pyruvate is decarboxylated, producing acetyl-CoA (and carbon dioxide and NADH). This irreversible reaction traps the acetyl-CoA within the mitochondria (the acetyl-CoA can only be transported out of the mitochondrial matrix under conditions of high oxaloacetate via the citrate shuttle, a TCA intermediate that is normally sparse). The carbon dioxide produced by this reaction is nonpolar and small, and can diffuse out of the mitochondria and out of the cell.
In prokaryotes, which have no mitochondria, this reaction is either carried out in the cytosol, or not at all.