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## Main Question or Discussion Point

**subspaces and dimension!!!!**

Consider two subspaces V and W of R^n ,where V is contained in W.

Why is dim(V)<= dim(W).....?

"<=" less than or equal to

- Thread starter leilei
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Consider two subspaces V and W of R^n ,where V is contained in W.

Why is dim(V)<= dim(W).....?

"<=" less than or equal to

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(v_1,v_2,...v_r,w) is a linearly independent set in W, so dim(W) is at least r+1 (could be more).

HallsofIvy

Science Advisor

Homework Helper

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By the way, do you see why saying "subspace V is a subset of subspace W" (they are both subspaces of some vector space U) is the same as saying "V is a subspace of W"?

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