Linear Algebra: Projection onto a subspace

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SUMMARY

The discussion focuses on the process of projecting a vector onto a subspace in linear algebra, specifically addressing the formula used for projection. The incorrect answer provided was Projection = (41/65)v1 + (26/5)v2, indicating a misunderstanding in applying the projection formula. Participants suggest that the conditions for vectors v1 and v2 must be orthogonal for the formula to be valid. An alternative method proposed involves finding a vector x that is perpendicular to the subspace V and using it to determine the projection.

PREREQUISITES
  • Understanding of vector spaces and subspaces
  • Familiarity with the projection formula in linear algebra
  • Knowledge of orthogonality and its implications in vector projections
  • Basic skills in manipulating fractions and equations
NEXT STEPS
  • Study the derivation and application of the projection formula in linear algebra
  • Learn about orthogonal vectors and their role in projections
  • Explore alternative methods for vector projection, including Gram-Schmidt orthogonalization
  • Practice problems involving projections onto subspaces with varying conditions
USEFUL FOR

Students studying linear algebra, educators teaching vector projections, and anyone looking to deepen their understanding of subspace properties and projection techniques.

Kisa30
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Homework Statement



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That is the question. The answer on the bottom is incorrect

Homework Equations



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I believe that is the formula that is supposed to be used.

The Attempt at a Solution



All I really did was plug in the equation into the formula but there is something I am missing because the answer is incorrect

Projection = (41/65)v1 + (26/5)v2
This is what I got after inserting the projection formula.
And in the first image, on the bottom it shows the final solutions I got.


Please help me figure out how to do this question and where I went wrong.

Thanks in advanced!
 
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Just a thought, but do you have to provide the solutions in a specific number format (i.e. rounded to a certain number of figures) or maybe as exact fractions?
 
I don't think it's important, no. =)
 
What conditions must v1 and v2 meet so that the formula can be used?

An alternative approach would be to find a vector x that's perpendicular to V, and find the projection of v onto x, and subtract that from v. What's left over will lie in the subspace V.
 
Apparently the problem is that it's not orthogonal.
 

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