
Orthogonal basis
Let
V = span
{
1 1 1 1
1 1 0 1
1 0 1 1
0 1 1 0
0 0 0 1 }
a) Find an orthogonal basis for V.
b) Write
(3
1
1
1
1 ) in terms of the new basis.
c) Find the projection of
( 2 )
( 1 )
( 0 )
( 1 )
( 2 ) onto V.
d) What is the distance between
( 2 )
( 1 )
( 0 )
( 1 )
( 2 ) and V?
To do this problem you need to find V. I don't know how to do that and I'm guessing once i do find V i won't be able to do the rest. At least not correctly without something to follow. Can someone please help me through this problem? TIA!!!