# 2 questions need help

• Jul 23rd 2006, 11:16 AM
luckyc1423
2 questions need help
1) IN C[ 0 , 1 ], find the projection of t + 1 onto t^2

2) Let W be the subspace of R^3 spanned by 1 and 0
0 1
1 0

A) find the distance between 3 and the nearest vector in W
2
1

B) write 3 as w + u, were w is in W and u is in W^(upside down T)
2
1

didnt know what the word for the symbol was, but it looks like an upside down T
• Jul 23rd 2006, 11:19 AM
luckyc1423
vectors got messed up
vectors got messed up when submited

2) vectors:

1 0
0 1
1 0

A) vectors:

3
2
1

B) vectors:

3
2
1
• Jul 23rd 2006, 01:14 PM
CaptainBlack
Quote:

Originally Posted by luckyc1423
1) IN C[ 0 , 1 ], find the projection of t + 1 onto t^2

Usually I would take the projection of $\bold u$ onto $\bold v$ to be $\frac{\langle \bold u,\bold v\rangle}{\|\bold v\|}\hat{\bold v}=\frac{\langle \bold u,\bold v\rangle}{\|\bold v\|^2} \bold v$.

On $C[0,1]$ we would normally use:

$
\langle \bold f, \bold g \rangle =\int_0^1 \overline{\bold{f}(x)}\bold{g}(x) dx
$

and:

$
\|\bold{f}\|=\langle \bold{f},\bold{f}\rangle^{1/2}
$

RonL