I can't wrap my head around these vector subtractions. They make 0 sense to me, can anyone help me get this simple step correct in my head? I'm getting nowhere since a hour.
Im trying to use the Gram-Schmidt on 3 vectors, but I can't get my head around the first equation of
$$u_2 = a_2 - \langle a_2,u_1 \rangle u_1$$
The final answer don't make any sense to me, I appended 2 pictures of 2 calculations that I just can't solve.
On the second equation I tried to multiply the $\frac12$ into the second vector and then tried to $v_1-v_2$, but it didn't get me the expected result.
Can anyone enlighten me this simple step?
Thanks!
$$ \left( \begin{array}{cc|c} 0\\ 1\\ 1 \end{array} \right) - \dfrac12 \left( \begin{array}{cc|c} 1\\0\\1 \end{array} \right) =\left( \begin{array}{cc|c} 0\\ 1\\ 1 \end{array} \right) - \left( \begin{array}{cc|c} \frac{1}2\\0\\ \frac12 \end{array} \right) = \left( \begin{array}{cc|c} \frac{-1}2\\1\\ \frac{1}2 \end{array} \right)= \dfrac12\left( \begin{array}{cc|c} {-1}\\2\\ {1} \end{array} \right)$$