# Thread: 2 questions need help

1. ## 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

2. ## 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

3. 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 $\displaystyle \bold u$ onto $\displaystyle \bold v$ to be $\displaystyle \frac{\langle \bold u,\bold v\rangle}{\|\bold v\|}\hat{\bold v}=\frac{\langle \bold u,\bold v\rangle}{\|\bold v\|^2} \bold v$.

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

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

and:

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

RonL