MathAlgebraLinear algebraLinear operators

Intersection and sums of subspaces

Dimensions

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Suppose we have two linear subspaces UU and WW of a vector space VV, such that U⊕W=VU \oplus W = V, and dim⁡U=2\dim U = 2, dim⁡W=3\dim W = 3.

What is dim⁡V\dim V?

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