Linear Algebra: Projection onto a subspace

[Kisa30]

Homework Statement

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

Homework Equations

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!

 

[Villhelm]

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?

 

[Kisa30]

I don't think it's important, no. =)

 

[vela]

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.

 

[Kisa30]

Apparently the problem is that it's not orthogonal.