Linear Algebra: Projection onto a subspace

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Homework Help Overview

The discussion revolves around a problem in linear algebra concerning the projection of a vector onto a subspace defined by vectors v1 and v2. Participants are exploring the correct application of the projection formula and the conditions under which it is valid.

Discussion Character

  • Exploratory, Assumption checking, Conceptual clarification

Approaches and Questions Raised

  • Participants discuss the original poster's attempt to apply the projection formula and express uncertainty about the correctness of their answer. Questions arise regarding the conditions that vectors v1 and v2 must satisfy for the formula to be applicable. An alternative method involving the projection onto a perpendicular vector is also suggested.

Discussion Status

The discussion is active, with participants providing thoughts on potential issues with the original poster's approach and exploring different methods of solving the problem. There is no explicit consensus, but various lines of reasoning are being examined.

Contextual Notes

Participants are considering whether specific formatting of the solution (such as rounding or using exact fractions) is required, and there is mention of the vectors not being orthogonal, which may affect the application of the projection formula.

Kisa30
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Homework Statement



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

Homework Equations



20276.nce108.gif

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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