Linear Algebra dimensions proof

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zcd
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Homework Statement


Let W1 and W2 be subspaces of a finite-dimensional vector space V. Determine necessary and sufficient conditions on W1 and W2 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(W1)=m and dim(W2)=n, n≥m and W1 is nested inside W2, so [tex]W_1 \subseteq W_2[/tex]?
 
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Answers and Replies

  • #2
ystael
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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]?

Yes.

If it is, is it possible to say that let dim(W1)=m and dim(W2)=n, n≥m and W1 is nested inside W2, so [tex]W_1 \subseteq W_2[/tex]?
"[tex]W_1 \subseteq W_2[/tex]" is a reasonable guess for what the right condition might be, but what you have written is not a proof of either direction of the implication.
 

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