To construct a matrix in Mathematica using predefined column vectors, the Transpose function is effective. For example, defining vectors as v1={a,b} and v2={c,d} allows the creation of the desired matrix with mat=Transpose[{v1,v2}], resulting in {{a,c},{b,d}}. However, if vectors are defined as v1={{a},{b}} and v2={{c},{d}}, using Transpose directly will not yield the intended matrix format. Instead, applying mat=Transpose[{Flatten[v1],Flatten[v2]}] successfully converts the nested vectors into the correct matrix format, producing {{a,c},{b,d}}. This approach clarifies how Mathematica handles vector dimensions and ensures the correct matrix structure.