Linear Algebra - dimension of orthogonal complement

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SUMMARY

The discussion centers on a linear algebra problem regarding the dimension of the orthogonal complement. The original poster believes their solution is correct, concluding with option C, while the answer key indicates the correct answer is D. This discrepancy raises questions about the accuracy of the answer key, prompting a request for verification from other forum members.

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  • Understanding of linear algebra concepts, specifically orthogonal complements.
  • Familiarity with dimension theory in vector spaces.
  • Ability to solve linear equations and interpret solution sets.
  • Knowledge of answer key verification methods in mathematical problems.
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  • Review the concept of orthogonal complements in linear algebra.
  • Study the properties of vector space dimensions.
  • Learn methods for verifying solutions against answer keys.
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Students studying linear algebra, educators teaching vector space concepts, and anyone involved in mathematical problem verification.

GuiltySparks
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I've attached a copy of the problem and my attempt at a solution.

This seems like a relatively straightforward question to me, but my answer seems to be the exact opposite of what the answer key says.

I reach the conclusion that the answer is C, but the answer is apparently D.

I'm beginning to think that the answer key is wrong. Can anybody verify my solution?
 

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I think your answer key is wrong.
 

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