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## Homework Statement

Let W

_{1}and W

_{2}be subspaces of a finite-dimensional vector space V. Determine necessary and sufficient conditions on W

_{1}and W

_{2}so that [tex]dim(W_1 \cap W_2)=dim(W_1)[/tex]

## Homework Equations

Replacement Theorem

## The Attempt at a Solution

To clarify on the question: is the problem asking for conditions such that [tex]condition\iff dim(W_1 \cap W_2)=dim(W_1)[/tex]?

If it is, is it possible to say that let dim(W

_{1})=m and dim(W

_{2})=n, n≥m and W

_{1}is nested inside W

_{2}, so [tex]W_1 \subseteq W_2[/tex]?

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