Vector Orthogonal projection: V = span( {2,0,0,4,0},{0,2,0,0,4} ), W={-4,0,4,-5,-1}

[Bob_2013]

Hi,

So I have that the subspace V = span( {2,0,0,4,0},{0,2,0,0,4} ) and W={-4,0,4,-5,-1}
I have found the orthogonal projection of W onto V giving {-14/5,-2/5,0,-28/5,-4/5}

However, I need to find the component of W orthogonal to V?
How would I go about doing this?

 

[Deleted member 4993]

Hi,

So I have that the subspace V = span( {2,0,0,4,0},{0,2,0,0,4} ) and W={-4,0,4,-5,-1}
I have found the orthogonal projection of W onto V giving {-14/5,-2/5,0,-28/5,-4/5}

However, I need to find the component of W orthogonal to V?
How would I go about doing this?

Hint:

Vector sum of [Projection of vector V in any direction l] & [Projection of vector V in any orthogonal direction to [FONT=&quot]l] = [vector [/FONT][FONT=&quot]V[/FONT][FONT=&quot]][/FONT]