- #1

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I have thius problem to solve. Please, help me!

1. Prove or disprove if U, V, W are subspaces of V for which

U (dir sum) W = V (dir sum) W then U=V

Thank you in advance!

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- Thread starter mivanova
- Start date

- #1

- 7

- 0

I have thius problem to solve. Please, help me!

1. Prove or disprove if U, V, W are subspaces of V for which

U (dir sum) W = V (dir sum) W then U=V

Thank you in advance!

- #2

Defennder

Homework Helper

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If it's indeed correct then think carefully about what this implies for any vector v in V and how it may be expressed as a unique sum of vectors v,w from V and W. What does it say about w?

And with this in mind, look at the left-hand side. Is this sufficient alone to conclude U=V?

- #3

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It's indeed (direct sum) and I think that the statement is it's not true. I can't prove it though.

Thanks!

- #4

Defennder

Homework Helper

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- #5

Defennder

Homework Helper

- 2,591

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What does that say about W? After you're done with this, think about the subspace spanned by U (dir sum) W, and what does it mean for U when the equality stated in the proposition holds.

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