Okay so I'm really confused with this one. Thankful if someone can help me out here.
W is a linear space spanned by (-1,0,0,1), (1,1,0,2). B = (0,2,5,-1).
a) Find the orthogonal projection of B onto W, using Gram-Schmidt process and the theorem below,
So first by calculating using the theorem:
\begin{align*}
b'= proj_wb = \frac{(b,v_1)}{||v_1||^2}v_1 +\frac{(b,v_2)}{||v_2||^2}v 2
\end{align*}
hence,
\begin{align*}
b' = -\frac{1}{2}v_1 + 0v_2 = -\frac{1}{2}(-1,0,0,1) + 0(1,1,0,2)\end{align*}\begin{align*}
= (\frac{1}{2},0,0,-\frac{1}{2})
\end{align*}
Is this the right way to do it?
And next part. Is the previous answer my new span when using gram-schmidt?
W is a linear space spanned by (-1,0,0,1), (1,1,0,2). B = (0,2,5,-1).
a) Find the orthogonal projection of B onto W, using Gram-Schmidt process and the theorem below,
So first by calculating using the theorem:
\begin{align*}
b'= proj_wb = \frac{(b,v_1)}{||v_1||^2}v_1 +\frac{(b,v_2)}{||v_2||^2}v 2
\end{align*}
hence,
\begin{align*}
b' = -\frac{1}{2}v_1 + 0v_2 = -\frac{1}{2}(-1,0,0,1) + 0(1,1,0,2)\end{align*}\begin{align*}
= (\frac{1}{2},0,0,-\frac{1}{2})
\end{align*}
Is this the right way to do it?
And next part. Is the previous answer my new span when using gram-schmidt?