Is the matrix P = [[0,0],[1,1]] an orthogonal projection?

[mistymoon_38]

[SOLVED] Quick Question: Is this matrix an orthogonal projection?

Homework Statement

P=[0 0 ]
[11]

Homework Equations

The Attempt at a Solution

Its orthogonal if the null space and range are perpendicular.
Range=[0 ]
[x+y]
null space=[x

 

[mistymoon_38]

null space=[x ]
[-x]??
So then its not orthogonal??

 

[Dick]

If you mean the range is spanned by the vector [0,1] and the null space is spanned by the vector [1,-1] (which I think you do mean) then yes, not orthogonal.